Question

triangle abc has coordinates a(2, 0), b(-1, 5), and c(4, 3). determine the coordinates of the vertices of the image after a translation along the vector <0, 2>.

a) a(2, 0), b(-1, -5), and c(4, -3)
b) a(-2, 0), b(1, 5), and c(-4, 3)
c) a(2, 2), b(-1, 7), and c(4, 5)
d) a(5, -4), b(2, 1), and c(7, -1)

Explanation:

Step1: Recall translation rule

For a translation along the vector $\langle0, 2
angle$, we add 0 to the $x$-coordinate and 2 to the $y$-coordinate of each vertex.

Step2: Translate vertex A

For $A(2,0)$, new $x = 2+0=2$, new $y=0 + 2=2$, so $A'=(2,2)$.

Step3: Translate vertex B

For $B(-1,5)$, new $x=-1 + 0=-1$, new $y=5 + 2=7$, so $B'=(-1,7)$.

Step4: Translate vertex C

For $C(4,3)$, new $x=4+0 = 4$, new $y=3+2=5$, so $C'=(4,5)$.

Answer:

C. $A'(2, 2), B'(-1, 7), C'(4, 5)$