Question

question 20 of 25
what is the transformation of a(6, 4) when dilated by a scale factor of ½, using the origin as the center of dilation?

a. a(-4, -6)

b. a(-3, -2)

c. a(3, 2)

d. a(12, 8)

Explanation:

Step1: Recall dilation formula

For a point \((x,y)\) dilated with scale factor \(k\) from the origin, the new point is \((kx,ky)\).

Step2: Apply the formula

Given \(A(6,4)\) and scale factor \(k = \frac{1}{2}\), calculate \(x'\) and \(y'\):
\(x' = 6\times\frac{1}{2}=3\)
\(y' = 4\times\frac{1}{2}=2\)
So the new point \(A'\) is \((3,2)\).

Answer:

C. \(A'(3,2)\)