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 and image on a separate sheet of paper.

s(0, 0), t(-4, 0), v(-8, -8), k = 1.25, centered at the origin

s(

,

)

t(

,

)

v(

,

)

Explanation:

Step1: Recall dilation rule

For a dilation centered at the origin with scale factor \( k \), the coordinates \((x,y)\) of a point transform to \((kx,ky)\).

Step2: Dilate point \( S(0,0) \)

Using the rule, for \( S(0,0) \) and \( k = 1.25 \), we have \( (1.25\times0,1.25\times0)=(0,0) \).

Step3: Dilate point \( T(-4,0) \)

For \( T(-4,0) \) and \( k = 1.25 \), calculate \( (1.25\times(-4),1.25\times0)=(-5,0) \).

Step4: Dilate point \( V(-8,-8) \)

For \( V(-8,-8) \) and \( k = 1.25 \), calculate \( (1.25\times(-8),1.25\times(-8))=(-10,-10) \).

Answer:

\( S(0, 0) \), \( T(-5, 0) \), \( V(-10, -10) \)