Question

for the set of triangle vertices, find the coordinates of the vertices of the image after a dilation by the given scale factor and center of dilation. then graph the preimage and image on a separate sheet of paper.
j(-3, 2), k(-1,1), l(-3, 0), k = 2, centered at j
j(
k(
l(

Explanation:

Step1: Recall Dilation Formula

The formula for dilation centered at a point \( (x_c, y_c) \) with scale factor \( k \) for a point \( (x, y) \) is \( (x', y')=(x_c + k(x - x_c), y_c + k(y - y_c)) \).

Step2: Find \( J' \)

For point \( J(-3, 2) \) (center of dilation), using the formula:
\( x'=-3 + 2(-3 - (-3))=-3+2(0)=-3 \)
\( y'=2 + 2(2 - 2)=2+2(0)=2 \)
So \( J'(-3, 2) \).

Step3: Find \( K' \)

For point \( K(-1, 1) \), \( x_c=-3,y_c = 2,k = 2 \):
\( x'=-3+2(-1-(-3))=-3 + 2(2)=-3 + 4 = 1 \)
\( y'=2+2(1 - 2)=2+2(-1)=2 - 2 = 0 \)
So \( K'(1, 0) \).

Step4: Find \( L' \)

For point \( L(-3, 0) \), \( x_c=-3,y_c = 2,k = 2 \):
\( x'=-3+2(-3-(-3))=-3+2(0)=-3 \)
\( y'=2+2(0 - 2)=2+2(-2)=2 - 4=-2 \)
So \( L'(-3, -2) \).

Answer:

\( J'(-3, 2) \), \( K'(1, 0) \), \( L'(-3, -2) \)