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(-8, 0), k(-4, 4), l(-2, 0), k = 0.5, centered at the origin
j( , )
k( , )
l( , )

Explanation:

Step1: Recall dilation formula

When dilating a point \((x, y)\) with a scale factor \(k\) centered at the origin, the new coordinates \((x', y')\) are given by \(x' = kx\) and \(y' = ky\).

Step2: Dilate point \(J(-8, 0)\)

For \(J(-8, 0)\) and \(k = 0.5\):
\(x' = 0.5\times(-8)= - 4\)
\(y' = 0.5\times0 = 0\)
So, \(J'\) is \((-4, 0)\).

Step3: Dilate point \(K(-4, 4)\)

For \(K(-4, 4)\) and \(k = 0.5\):
\(x' = 0.5\times(-4)= - 2\)
\(y' = 0.5\times4 = 2\)
So, \(K'\) is \((-2, 2)\).

Step4: Dilate point \(L(-2, 0)\)

For \(L(-2, 0)\) and \(k = 0.5\):
\(x' = 0.5\times(-2)= - 1\)
\(y' = 0.5\times0 = 0\)
So, \(L'\) is \((-1, 0)\).

Answer:

\(J'(-4, 0)\)
\(K'(-2, 2)\)
\(L'(-1, 0)\)