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Math  /  Geometry

QuestionFigure II is a translation image of Figure I. Write a rule to describe the translation.
The translation rule is (x,y)→h+(□),y+(□)(x, y) \rightarrow h+(\square), y+(\square). w an example Get more help - Clear all Check answer

Studdy Solution

STEP 1

1. Figure I and Figure II are geometric figures (triangles) located on a coordinate plane.
2. The translation rule will be determined by the horizontal and vertical shifts needed to map points from Figure I to corresponding points in Figure II.
3. We will use the coordinates of corresponding vertices from both figures to determine the translation rule.

STEP 2

1. Identify corresponding points in Figure I and Figure II.
2. Calculate the horizontal shift (change in x-coordinates) and the vertical shift (change in y-coordinates) for one pair of corresponding points.
3. Verify that the same shifts apply to the other pairs of corresponding points.
4. Formulate the translation rule and present it in the required format.

STEP 3

Identify corresponding points in Figure I and Figure II.
Figure I vertices: A(−5,4)A(-5, 4), B(−3,4)B(-3, 4), C(−4,6)C(-4, 6) Figure II vertices: A′(2,−1)A'(2, -1), B′(4,−1)B'(4, -1), C′(3,1)C'(3, 1)

STEP 4

Calculate the horizontal shift (change in x-coordinates) and the vertical shift (change in y-coordinates) for one pair of corresponding points.
For point A to A': Δx=xA′−xA=2−(−5)=2+5=7 \Delta x = x_{A'} - x_A = 2 - (-5) = 2 + 5 = 7 Δy=yA′−yA=−1−4=−5 \Delta y = y_{A'} - y_A = -1 - 4 = -5

STEP 5

Verify that the same shifts apply to the other pairs of corresponding points.
For point B to B': Δx=xB′−xB=4−(−3)=4+3=7 \Delta x = x_{B'} - x_B = 4 - (-3) = 4 + 3 = 7 Δy=yB′−yB=−1−4=−5 \Delta y = y_{B'} - y_B = -1 - 4 = -5
For point C to C': Δx=xC′−xC=3−(−4)=3+4=7 \Delta x = x_{C'} - x_C = 3 - (-4) = 3 + 4 = 7 Δy=yC′−yC=1−6=−5 \Delta y = y_{C'} - y_C = 1 - 6 = -5

STEP 6

Formulate the translation rule and present it in the required format.
The translation rule is: (x,y)→(x+7,y−5) (x, y) \rightarrow (x + 7, y - 5)

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