Question

graph the image of kite jklm after a dilation with a scale factor of 1/4, centered at the origin. match the appropriate coordinate for jklm. drag & drop the answer

Explanation:

Step1: Recall dilation formula

For a dilation centered at the origin with scale - factor $k$, if a point $(x,y)$ is dilated, the new point $(x',y')$ is given by $(x',y')=(k x,k y)$.

Step2: Identify original coordinates

Assume the original coordinates of the kite vertices: Let's say $J(x_J,y_J)$, $K(x_K,y_K)$, $L(x_L,y_L)$, $M(x_M,y_M)$. From the graph, if $J(4, - 8)$, $K(8,0)$, $L(4,8)$, $M(-8,0)$ and $k = \frac{1}{4}$.

Step3: Calculate new coordinates for $J'$

$x_{J'}=\frac{1}{4}\times4 = 1$, $y_{J'}=\frac{1}{4}\times(-8)=-2$. So $J'=(1,-2)$.

Step4: Calculate new coordinates for $K'$

$x_{K'}=\frac{1}{4}\times8 = 2$, $y_{K'}=\frac{1}{4}\times0 = 0$. So $K'=(2,0)$.

Step5: Calculate new coordinates for $L'$

$x_{L'}=\frac{1}{4}\times4 = 1$, $y_{L'}=\frac{1}{4}\times8 = 2$.

Step6: Calculate new coordinates for $M'$

$x_{M'}=\frac{1}{4}\times(-8)=-2$, $y_{M'}=\frac{1}{4}\times0 = 0$. So $M'=(-2,0)$.

Answer:

$J'$: $(1,-2)$
$K'$: $(2,0)$
$L'$: $(1,2)$
$M'$: $(-2,0)$