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10.04 AM Wed Apr?3
CHARLOTTE HIGGINS's practice
S. 2 Dilations: graph the image
Graph the image of square KLMN after a dilation with a scale factor of 2 , centered at the origin.
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$10$ . $04$ AM Wed Apr? $3$ $\newline$ CHARLOTTE HIGGINS's practice $\newline$ S. $2$ Dilations: graph the image $\newline$ Graph the image of square KLMN after a dilation with a scale factor of $2$ , centered at the origin. $\newline$ Submit $\newline$ Not ready yet?

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Dilations and parallel lines

Full solution

Q.

10

.

04

AM Wed Apr?

3

\newline

CHARLOTTE HIGGINS's practice

\newline

S.

2

Dilations: graph the image

\newline

Graph the image of square KLMN after a dilation with a scale factor of

2

, centered at the origin.

\newline

Submit

\newline

Not ready yet?

Identify Coordinates: Identify the coordinates of square $KLMN$ . Assume vertices $K(1,1)$ , $L(1,3)$ , $M(3,3)$ , and $N(3,1)$ for simplicity.
Apply Dilation Formula: Apply the dilation formula for each vertex. The formula for dilation centered at the origin is $(x', y') = (kx, ky)$ , where $k$ is the scale factor.
Calculate New Coordinates: Calculate the new coordinates for each vertex using the scale factor of $2$ . For $K(1,1)$ , the new coordinates are $(2\times 1, 2\times 1) = (2, 2)$ .
Plot New Vertices: Continue with vertex $L(1,3)$ . New coordinates are $(2\times1, 2\times3) = (2, 6)$ .
Plot New Vertices: Continue with vertex $L(1,3)$ . New coordinates are $(2\times1, 2\times3) = (2, 6)$ . For vertex $M(3,3)$ , calculate $(2\times3, 2\times3) = (6, 6)$ .
Plot New Vertices: Continue with vertex $L(1,3)$ . New coordinates are $(2\times1, 2\times3) = (2, 6)$ . For vertex $M(3,3)$ , calculate $(2\times3, 2\times3) = (6, 6)$ . Lastly, for vertex $N(3,1)$ , calculate $(2\times3, 2\times1) = (6, 2)$ .
Plot New Vertices: Continue with vertex $L(1,3)$ . New coordinates are $(2\times1, 2\times3) = (2, 6)$ . For vertex $M(3,3)$ , calculate $(2\times3, 2\times3) = (6, 6)$ . Lastly, for vertex $N(3,1)$ , calculate $(2\times3, 2\times1) = (6, 2)$ . Plot the new vertices on a graph: $K'(2,2)$ , $L'(2,6)$ , $M'(6,6)$ , and $N'(6,2)$ . Draw lines connecting these points to form the dilated square.

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