Question

graph the image of square jklm after a dilation with a scale factor of $\frac{1}{5}$ centered at the origin.

Explanation:

Step1: Recall dilation rule

For a dilation centered at the origin with scale - factor $k=\frac{1}{5}$, if a point $(x,y)$ is dilated, the new point $(x',y')$ has coordinates $x' = kx$ and $y'=ky$.

Step2: Assume coordinates of square vertices

Let's assume the vertices of square $JKLM$ have coordinates $J(x_1,y_1)$, $K(x_2,y_2)$, $L(x_3,y_3)$, $M(x_4,y_4)$. For example, if $J(- 10,-10)$, $K(10,-10)$, $L(10,10)$, $M(-10,10)$.

Step3: Calculate new coordinates

For point $J(-10,-10)$:
$x_J'=\frac{1}{5}\times(-10)= - 2$
$y_J'=\frac{1}{5}\times(-10)=-2$
For point $K(10,-10)$:
$x_K'=\frac{1}{5}\times10 = 2$
$y_K'=\frac{1}{5}\times(-10)=-2$
For point $L(10,10)$:
$x_L'=\frac{1}{5}\times10 = 2$
$y_L'=\frac{1}{5}\times10 = 2$
For point $M(-10,10)$:
$x_M'=\frac{1}{5}\times(-10)=-2$
$y_M'=\frac{1}{5}\times10 = 2$

Step4: Graph new square

Plot the new points $J'(-2,-2)$, $K'(2,-2)$, $L'(2,2)$, $M'(-2,2)$ and connect them to form the dilated square.

Answer:

Graph the square with vertices $(-2,-2)$, $(2,-2)$, $(2,2)$, $(-2,2)$.