Question

leila uses the photo app to resize a photo of her dog, represented by figure jkl m. she dilates the photo using a scale factor of $\frac{1}{2}$ with a center of dilation at point j. what are the coordinates of the image of point k? (-4,5) (-3,4) (-4,8) (-1,4)

Explanation:

Step1: Identify the coordinates of point J and K

Let's assume the coordinates of point J are $(-6,8)$ and of point K are $(-2,8)$ from the graph.

Step2: Use the dilation formula

The formula for dilation with center $(x_0,y_0)$ and scale - factor $k$ for a point $(x,y)$ is $(x',y')=(x_0 + k(x - x_0),y_0 + k(y - y_0))$. Here, $(x_0,y_0)=(-6,8)$ (coordinates of J), $k=\frac{1}{2}$, and $(x,y)=(-2,8)$ (coordinates of K).
First, for the x - coordinate:
$x'=-6+\frac{1}{2}(-2+6)=-6 + \frac{1}{2}(4)=-6 + 2=-4$.
Second, for the y - coordinate:
$y'=8+\frac{1}{2}(8 - 8)=8+0 = 8$.

Answer:

$(-4,8)$