Question

multiple choice: the vertices of △abc are a(-4,2), b(6,6), c(2,7). a translation maps point a to the point a(6, - 3). if b and c are mapped by the same translation, what are the coordinates of b and c? a. b(-4,11) and c(-8,-12) b. b(8,5) and c(4,6) c. b(12,3) and c(8,4) d. b(16,1) and c(12,2)

Explanation:

Step1: Find translation rule

To find the translation rule, we look at the change from point A(-4, 2) to A'(6, - 3). The change in the x - coordinate is \(6-(-4)=10\), and the change in the y - coordinate is \(-3 - 2=-5\). So the translation rule is \((x,y)\to(x + 10,y-5)\).

Step2: Translate point B

Given B(6,6), applying the translation rule: \(x=6,y = 6\). The new x - coordinate of B' is \(6 + 10=16\), and the new y - coordinate of B' is \(6-5 = 1\).

Step3: Translate point C

Given C(2,7), applying the translation rule: \(x = 2,y=7\). The new x - coordinate of C' is \(2+10 = 12\), and the new y - coordinate of C' is \(7-5=2\).

Answer:

D. B'(16,1) and C'(12,2)