Transformations

Problem 301

Find the translation from triangle $K M N$ with vertices $K(12,3), M(-5,2), N(8,-4)$ to $K^{\prime}(18,0), M^{\prime}(1,-1), N^{\prime}(14,-7)$ .

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Problem 302

Describe the rotation that transforms triangle $P Q R$ with vertices $P(9,-2)$ , $Q(1,0)$ , $R(-7,3)$ to $P^{\prime}(-9,2)$ , $Q^{\prime}(-1,0)$ , $R^{\prime}(7,-3)$ .

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Problem 303

Find the rotation that transforms triangle $PQR$ with vertices $P(9,-2)$ , $Q(1,0)$ , $R(-7,3)$ to $P'(-9,2)$ , $Q'(-1,0)$ , $R'(7,-3)$ .

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Problem 304

Reflect triangle $G H J$ with vertices $G(-5,3), H(2,6), J(-6,2)$ to get $G^{\prime}(5,3), H^{\prime}(-2,6), J^{\prime}(6,2)$ .

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Problem 305

Reflect triangle STW across the x-axis to get triangle S'T'W' with vertices $S'(15,6)$ , $T'(-2,-3)$ , $W'(-8,8)$ .

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Problem 306

+0 pts / 1500
Question 4 of 15
Consider the structure $Y-\ddot{X}-Y$ If the symbol X represents a central atom, Y represents outer atoms, and Z represents lone pairs on the central atom, the structure could be abbreviated as $\mathrm{XY}_{2} \mathrm{Z}_{2}$ . Classify each molecule according to its shape. Answer Bank $\mathrm{XY}_{3} \mathrm{Z}_{2}$ $\mathrm{XY}_{5} \mathrm{Z}$ $\mathrm{XY}_{3} \mathrm{Z}$ $\mathrm{XY}_{2} \mathrm{Z}$ $\mathrm{XY}_{2} \mathrm{Z}_{3}$ $\mathrm{XY}_{2} \mathrm{Z}_{2}$ $\mathrm{XY}_{4} \mathrm{Z}_{2}$ $\mathrm{XY}_{4} \mathrm{Z}$

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Problem 307

Find the coordinates of $\mathrm{C}^{\prime}$ if point C is (0, -3) and transformed by $(x, y) \longrightarrow (y+4,-x)$ .

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Problem 308

Translation Reflection Rotation None of these

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Problem 309

Question 10 : A rectangular metal frame LMOK is placed between two long and parallel straight wires, all of which are in the same plane as the figure, if the same current intensity I passes through each of them, then the frame ..... 1- rotates around an axis parallel to the two wires 2- is not affected by a torque 3- moves upwards in a direction parallel to the two wires 4- rotates around an axis perpendicular to the two wires

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Problem 310

3. Look at $\triangle S T U$ on this coordinate grid.
Suppose that $\triangle S^{\prime} T^{\prime} U^{\prime}$ is the result of a dilation of $\triangle S T U$ with center $T$ and scale factor 2 . What are the coordinates of point S?
A $(4,2)$ B. $(0,-3)$ c. $(3,4)$
D $(6,9)$

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Problem 311

Translating $\triangle L M N$ to the right 8 units and downward 1 unit, we get its image $\triangle L^{\prime} M^{\prime} N^{\prime}$ .
Note that $\triangle L M N$ has vertices $L(-3,6), M(-5,4)$ , and $N(-1,1)$ . Also, note that $\Delta L^{\prime} M^{\prime} N^{\prime}$ has vertices $L^{\prime}(5,5), M^{\prime}(3,3)$ , and $N^{\prime}(7,0)$ . Complete the following.

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Problem 312

Identify the graph of the function from reflecting $f(x)=\frac{1}{4}(8)^{x}$ across the y-axis and x-axis.

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Problem 313

Write the coordinates of the vertices after a translation 2 units left. $K^{\prime}(\square, \square)$

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Problem 314

Draw $\Delta L M N$ with vertices $L(3,-1), M(8,-2)$ , and $N(6,2)$ . Find the coordinates of the vertices after a $90^{\circ}$ rotation about the origin and about each of the poil and $N$ .
What are the coordinates of the points after a $90^{\circ}$ rotation about the origin? $\mathrm{L}^{\prime}(1,3), \mathrm{M}^{\prime}(2,8), \mathrm{N}^{\prime}(-2,6)$ What are the coordinates of the points after a $90^{\circ}$ rotation about $L$ ? $\mathrm{L}^{\prime}(3,-1), \mathrm{M}^{\prime}(4,4), \mathrm{N}^{\prime}(0,2)$
What are the coordinates of the points after a $90^{\circ}$ rotation about $M$ ? $\mathrm{L}^{\prime}(7,-7), \mathrm{M}^{\prime}(8,-2), \mathrm{N}^{\prime}(4,-4)$ What are the coordinates of the points after a $90^{\circ}$ rotation about $N$ ? L' $\square$ , M' $\square$ , $\mathrm{N}^{\prime}$ $\square$

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Problem 315

Write the coordinates of the vertices after a rotation $90^{\circ}$ counterclockwise around the origin. $\begin{array}{l} J^{\prime}(\sqrt{1}, \\ K^{\prime}(, \quad, \quad) \\ L^{\prime}(\square, \square) \\ M^{\prime}(\square, \square) \end{array}$

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Problem 316

Translate a figure 1 unit right and 3 units down. Plot the new points of the translated figure.

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Problem 317

Siva sees a scale drawing half the width and height of the original. Is the scale factor $\frac{1}{2}$ correct? Explain.

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Problem 318

(文) The point $U(-1,-3)$ is reflected over the $x$ -axis. What are the coordinates of the resulting point, U'? $U^{\prime}(\square, \square)$

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Problem 319

問題 64 平面において, 原点を中心に $\frac{\pi}{6}$ 回転移動させてから, 直線 $y=-2 x$ に関して対称移動させても動かない点を求めよ。

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Problem 320

浙江科技大学考试试卷
4. The state of plane stress at a point with respect to the $x y$ -axes is shown in Figure. Determine the principal stresses and principal planes. Show the results on a sketch of an element aligned with the principal directions. (25 points）

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Problem 321

as an verierid prets reflection of point $A \mathrm{~ms}$ an ondered pair.
2. Use the graph to answer parts (a)-(k) as is corternd peit. as an endered patu. b. Reflect point $F$ across the $x$ -avis and label the reflection H. Write the coordinates of point $F$ as an ordered pair. *eninco mactice

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Problem 322

If this triangle is reflected over the line $y=k$ , what are the coordinates for $y$ ? $(-2,-6)$ $(-6.2)$ 125 (6.2)

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Problem 323

If you rotate this triangle 180 degrees counterclockwise, what are the coordinates for point $K$ $(6,-6)$ $(-6,6)$ $(-6,-6)$ $(6,6)$

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Problem 324

Determine the coordinate of the point $P(x, y)$ after a rotation of 40 degrees about $(0,0)$ , from the point $(5,0)$ . Round to 1 decimal place.

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Problem 325

Find the new coordinates of the point $(2,-6)$ after applying the transformations $R_{270^{\circ}}$ and then $r_{\mathrm{y} \text{-axis}}$ .

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Problem 326

A hexagon is graphed on a coordinate grid and then was rotated $90^{\circ}$ counterclockwise with the origin as the center of rotation to create a new figure. If a vertex of the original hexagon was located at $(3,-9)$ , which ordered pair represents the vertex of the new hexagon after th transformation? $(3,9)$ $(9,3)$ $(-3,-9)$ $(-9,-3)$

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Problem 327

Considere el plano $x-2 y+2 z=1$ y los puntos $A(-1,2,3) \quad B(1,4,4)$ que pertenecen a dicho plano. Si $A$ es el centro del cuadrad̃o y $B$ es un vértice, determine los otros vértices.

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Problem 328

rx 5 18) $\Delta$ (8)

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Problem 329

Select the correct answer from eacn arop-uvwirimitu.
There are seven lines of reflection across which the regular polygon $A B C D E F G$ can reflect to map onto itself. One of them is a of

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Problem 330

Find the standard matrix for the linear transformation $T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ that rotates points by $-\frac{5 \pi}{4}$ radians. $A=$

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Problem 331

Find the standard matrix for the linear transformation $T$ that rotates points in $\mathbb{R}^2$ by $-\frac{\pi}{2}$ radians. $A =$ (Enter exact values for each matrix element.)

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1 2 3 4

Transformations

Problem 301

Find the translation from triangle KMNK M NKMN with vertices K(12,3),M(−5,2),N(8,−4)K(12,3), M(-5,2), N(8,-4)K(12,3),M(−5,2),N(8,−4) to K′(18,0),M′(1,−1),N′(14,−7)K^{\prime}(18,0), M^{\prime}(1,-1), N^{\prime}(14,-7)K′(18,0),M′(1,−1),N′(14,−7).

Problem 302

Describe the rotation that transforms triangle PQRP Q RPQR with vertices P(9,−2)P(9,-2)P(9,−2), Q(1,0)Q(1,0)Q(1,0), R(−7,3)R(-7,3)R(−7,3) to P′(−9,2)P^{\prime}(-9,2)P′(−9,2), Q′(−1,0)Q^{\prime}(-1,0)Q′(−1,0), R′(7,−3)R^{\prime}(7,-3)R′(7,−3).

Problem 303

Find the rotation that transforms triangle PQRPQRPQR with vertices P(9,−2)P(9,-2)P(9,−2), Q(1,0)Q(1,0)Q(1,0), R(−7,3)R(-7,3)R(−7,3) to P′(−9,2)P'(-9,2)P′(−9,2), Q′(−1,0)Q'(-1,0)Q′(−1,0), R′(7,−3)R'(7,-3)R′(7,−3).

Problem 304

Reflect triangle GHJG H JGHJ with vertices G(−5,3),H(2,6),J(−6,2)G(-5,3), H(2,6), J(-6,2)G(−5,3),H(2,6),J(−6,2) to get G′(5,3),H′(−2,6),J′(6,2)G^{\prime}(5,3), H^{\prime}(-2,6), J^{\prime}(6,2)G′(5,3),H′(−2,6),J′(6,2).

Problem 305

Reflect triangle STW across the x-axis to get triangle S'T'W' with vertices S′(15,6)S'(15,6)S′(15,6), T′(−2,−3)T'(-2,-3)T′(−2,−3), W′(−8,8)W'(-8,8)W′(−8,8).

Problem 306

Problem 307

Find the coordinates of C′\mathrm{C}^{\prime}C′ if point C is (0, -3) and transformed by (x,y)⟶(y+4,−x)(x, y) \longrightarrow (y+4,-x)(x,y)⟶(y+4,−x).

Problem 308

Translation Reflection Rotation None of these

Problem 309

Problem 310

Problem 311

Problem 312

Identify the graph of the function from reflecting f(x)=14(8)xf(x)=\frac{1}{4}(8)^{x}f(x)=41​(8)x across the y-axis and x-axis.

Problem 313

Write the coordinates of the vertices after a translation 2 units left. K′(□,□)K^{\prime}(\square, \square)K′(□,□)

Problem 314

Problem 315

Problem 316

Translate a figure 1 unit right and 3 units down. Plot the new points of the translated figure.

Problem 317

Siva sees a scale drawing half the width and height of the original. Is the scale factor 12\frac{1}{2}21​ correct? Explain.

Problem 318

(文) The point U(−1,−3)U(-1,-3)U(−1,−3) is reflected over the xxx-axis. What are the coordinates of the resulting point, U'? U′(□,□)U^{\prime}(\square, \square)U′(□,□)

Problem 319

問題 64 平面において, 原点を中心に π6\frac{\pi}{6}6π​ 回転移動させてから, 直線 y=−2xy=-2 xy=−2x に関して対称移動させても動かない点を求めよ。

Problem 320

浙江科技大学考试试卷4. The state of plane stress at a point with respect to the xyx yxy-axes is shown in Figure. Determine the principal stresses and principal planes. Show the results on a sketch of an element aligned with the principal directions. (25 points）

Problem 321

Problem 322

If this triangle is reflected over the line y=ky=ky=k, what are the coordinates for yyy ? (−2,−6)(-2,-6)(−2,−6) (−6.2)(-6.2)(−6.2) 125 (6.2)

Problem 323

If you rotate this triangle 180 degrees counterclockwise, what are the coordinates for point KKK (6,−6)(6,-6)(6,−6) (−6,6)(-6,6)(−6,6) (−6,−6)(-6,-6)(−6,−6) (6,6)(6,6)(6,6)

Problem 324

Determine the coordinate of the point P(x,y)P(x, y)P(x,y) after a rotation of 40 degrees about (0,0)(0,0)(0,0), from the point (5,0)(5,0)(5,0). Round to 1 decimal place.

Problem 325

Find the new coordinates of the point (2,−6)(2,-6)(2,−6) after applying the transformations R270∘R_{270^{\circ}}R270∘​ and then ry-axisr_{\mathrm{y} \text{-axis}}ry-axis​.

Problem 326

Problem 327

Considere el plano x−2y+2z=1x-2 y+2 z=1x−2y+2z=1 y los puntos A(−1,2,3)B(1,4,4)A(-1,2,3) \quad B(1,4,4)A(−1,2,3)B(1,4,4) que pertenecen a dicho plano. Si AAA es el centro del cuadrad̃o y BBB es un vértice, determine los otros vértices.

Problem 328

rx 5 18) Δ\DeltaΔ (8)

Problem 329

Select the correct answer from eacn arop-uvwirimitu.There are seven lines of reflection across which the regular polygon ABCDEFGA B C D E F GABCDEFG can reflect to map onto itself. One of them is a of

Problem 330

Find the standard matrix for the linear transformation T:R2→R2T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}T:R2→R2 that rotates points by −5π4-\frac{5 \pi}{4}−45π​ radians. A=A=A=

Problem 331

Find the standard matrix for the linear transformation TTT that rotates points in R2\mathbb{R}^2R2 by −π2-\frac{\pi}{2}−2π​ radians. A= A = A= (Enter exact values for each matrix element.)

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Find the translation from triangle $K M N$ with vertices $K(12,3), M(-5,2), N(8,-4)$ to $K^{\prime}(18,0), M^{\prime}(1,-1), N^{\prime}(14,-7)$ .

Describe the rotation that transforms triangle $P Q R$ with vertices $P(9,-2)$ , $Q(1,0)$ , $R(-7,3)$ to $P^{\prime}(-9,2)$ , $Q^{\prime}(-1,0)$ , $R^{\prime}(7,-3)$ .

Find the rotation that transforms triangle $PQR$ with vertices $P(9,-2)$ , $Q(1,0)$ , $R(-7,3)$ to $P'(-9,2)$ , $Q'(-1,0)$ , $R'(7,-3)$ .

Reflect triangle $G H J$ with vertices $G(-5,3), H(2,6), J(-6,2)$ to get $G^{\prime}(5,3), H^{\prime}(-2,6), J^{\prime}(6,2)$ .

Reflect triangle STW across the x-axis to get triangle S'T'W' with vertices $S'(15,6)$ , $T'(-2,-3)$ , $W'(-8,8)$ .

Find the coordinates of $\mathrm{C}^{\prime}$ if point C is (0, -3) and transformed by $(x, y) \longrightarrow (y+4,-x)$ .

Identify the graph of the function from reflecting $f(x)=\frac{1}{4}(8)^{x}$ across the y-axis and x-axis.

Write the coordinates of the vertices after a translation 2 units left. $K^{\prime}(\square, \square)$

Siva sees a scale drawing half the width and height of the original. Is the scale factor $\frac{1}{2}$ correct? Explain.

(文) The point $U(-1,-3)$ is reflected over the $x$ -axis. What are the coordinates of the resulting point, U'? $U^{\prime}(\square, \square)$

問題 64 平面において, 原点を中心に $\frac{\pi}{6}$ 回転移動させてから, 直線 $y=-2 x$ に関して対称移動させても動かない点を求めよ。

浙江科技大学考试试卷
4. The state of plane stress at a point with respect to the $x y$ -axes is shown in Figure. Determine the principal stresses and principal planes. Show the results on a sketch of an element aligned with the principal directions. (25 points）

If this triangle is reflected over the line $y=k$ , what are the coordinates for $y$ ? $(-2,-6)$ $(-6.2)$ 125 (6.2)

If you rotate this triangle 180 degrees counterclockwise, what are the coordinates for point $K$ $(6,-6)$ $(-6,6)$ $(-6,-6)$ $(6,6)$

Determine the coordinate of the point $P(x, y)$ after a rotation of 40 degrees about $(0,0)$ , from the point $(5,0)$ . Round to 1 decimal place.

Find the new coordinates of the point $(2,-6)$ after applying the transformations $R_{270^{\circ}}$ and then $r_{\mathrm{y} \text{-axis}}$ .

Considere el plano $x-2 y+2 z=1$ y los puntos $A(-1,2,3) \quad B(1,4,4)$ que pertenecen a dicho plano. Si $A$ es el centro del cuadrad̃o y $B$ es un vértice, determine los otros vértices.

rx 5 18) $\Delta$ (8)

Select the correct answer from eacn arop-uvwirimitu.
There are seven lines of reflection across which the regular polygon $A B C D E F G$ can reflect to map onto itself. One of them is a of

Find the standard matrix for the linear transformation $T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ that rotates points by $-\frac{5 \pi}{4}$ radians. $A=$

Find the standard matrix for the linear transformation $T$ that rotates points in $\mathbb{R}^2$ by $-\frac{\pi}{2}$ radians. $A =$ (Enter exact values for each matrix element.)