Question

write the coordinates of the vertices after a dilation with a scale factor of $\frac{1}{2}$, centered at the origin.
a(
b(
c(

Explanation:

Step1: Identify original coordinates

Assume \(A(-4, -6)\), \(B(0, -6)\), \(C(0, - 10)\)

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor \(k=\frac{1}{2}\), the formula for the coordinates of a point \((x,y)\) after dilation is \((kx,ky)\).
For point \(A\): \(x=-4,y = - 6\), after dilation \(A'(\frac{1}{2}\times(-4),\frac{1}{2}\times(-6))=(-2,-3)\)
For point \(B\): \(x = 0,y=-6\), after dilation \(B'(\frac{1}{2}\times0,\frac{1}{2}\times(-6))=(0,-3)\)
For point \(C\): \(x = 0,y=-10\), after dilation \(C'(\frac{1}{2}\times0,\frac{1}{2}\times(-10))=(0,-5)\)

Answer:

\(A'(-2,-3)\)
\(B'(0,-3)\)
\(C'(0,-5)\)