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: Understand the translation rule

A translation along the vector $\langle a,b
angle$ changes the coordinates of a point $(x,y)$ to $(x + a,y + b)$. Here $a = 0$ and $b=2$.

Step2: Apply the rule to point A

For point $A(2,0)$: $x=2,y = 0$. Using the rule $(x + 0,y+2)$, we get $A'(2,0 + 2)=(2,2)$.

Step3: Apply the rule to point B

For point $B(-1,5)$: $x=-1,y = 5$. Using the rule $(x + 0,y + 2)$, we get $B'(-1,5 + 2)=(-1,7)$.

Step4: Apply the rule to point C

For point $C(4,3)$: $x = 4,y=3$. Using the rule $(x + 0,y + 2)$, we get $C'(4,3+2)=(4,5)$.

Answer:

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