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 ⟨3, -4⟩

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

To translate a point $(x,y)$ along the vector $\langle a,b
angle$, the new - coordinates $(x',y')$ are given by $(x + a,y + b)$.

Step2: Translate point A

For point $A(2,0)$ and vector $\langle3,-4
angle$, we have $x = 2,y = 0,a = 3,b=-4$. Then $x'=2 + 3=5$ and $y'=0+( - 4)=-4$. So $A'=(5,-4)$.

Step3: Translate point B

For point $B(-1,5)$ and vector $\langle3,-4
angle$, we have $x=-1,y = 5,a = 3,b=-4$. Then $x'=-1 + 3=2$ and $y'=5+( - 4)=1$. So $B'=(2,1)$.

Step4: Translate point C

For point $C(4,3)$ and vector $\langle3,-4
angle$, we have $x = 4,y = 3,a = 3,b=-4$. Then $x'=4 + 3=7$ and $y'=3+( - 4)=-1$. So $C'=(7,-1)$.

Answer:

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