Math / Geometry

Questionadfs dekalbschools. Imagine Learning
Graph the image of kite QRST after a dilation with a scale factor of 2 , centered at the origin.

Studdy Solution

STEP 1

1. The dilation is centered at the origin $(0, 0)$ .
2. The scale factor for the dilation is $2$ .
3. The original vertices of kite QRST are given as $Q(-1, -5)$ , $R(1, 2)$ , $S(0, 4)$ , and $T(-2, 2)$ .

STEP 2

1. Understand the concept of dilation.
2. Apply the dilation transformation to each vertex.
3. Plot the new vertices on the coordinate grid.

STEP 3

Understand the concept of dilation:
A dilation with a scale factor $k$ centered at the origin transforms a point $(x, y)$ to $(kx, ky)$ .

STEP 4

Apply the dilation transformation to each vertex:
- For $Q(-1, -5)$ : $ Q' = (2 \times -1, 2 \times -5) = (-2, -10) \]
- For $R(1, 2)$ : $ R' = (2 \times 1, 2 \times 2) = (2, 4) \]
- For $S(0, 4)$ : $ S' = (2 \times 0, 2 \times 4) = (0, 8) \]
- For $T(-2, 2)$ : $ T' = (2 \times -2, 2 \times 2) = (-4, 4) \]

STEP 5

Plot the new vertices on the coordinate grid:
- Plot $Q'(-2, -10)$ - Plot $R'(2, 4)$ - Plot $S'(0, 8)$ - Plot $T'(-4, 4)$
Connect the vertices $Q'R'S'T'$ to form the dilated kite.
The image of kite QRST after the dilation is plotted with vertices at:
$Q'(-2, -10), R'(2, 4), S'(0, 8), T'(-4, 4)$

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