Question

△abc has vertices a(3,0), b(4,2), and c(5,1). if a dilation centered at the origin with a scale factor of 3 is applied, what is the coordinate of b? (1, -1) (7, 5) (5, 3) (12, 6)

Explanation:

Step1: Recall Dilation Rule

For a dilation centered at the origin with scale factor \( k \), the rule is \((x,y)\to(kx,ky)\).

Step2: Apply to Point B

Point \( B \) is \((4,2)\). Multiply \( x \)-coordinate: \( 4\times3 = 12 \). Multiply \( y \)-coordinate: \( 2\times3 = 6 \). So \( B'=(12,6) \).

Answer:

(12, 6)