Question

a translation is used to map (a(-5,13)) to (a(2,9)). if the same translation is used to map (b(4, - 2)), then its image (b) would be
(b(7,-4))
(b(11,-6))
(b(8,-5))
(b(-3,2))

Explanation:

Step1: Find the translation rule

To find the translation rule from $A(-5,13)$ to $A'(2,9)$, we find the change in the $x$ - coordinate and the change in the $y$ - coordinate.
The change in the $x$ - coordinate: $\Delta x=2-(-5)=2 + 5=7$.
The change in the $y$ - coordinate: $\Delta y=9 - 13=-4$.
So the translation rule is $(x,y)\to(x + 7,y-4)$.

Step2: Apply the translation rule to point $B$

Given $B(4,-2)$, for the $x$ - coordinate of $B'$: $x_{B'}=4 + 7=11$.
For the $y$ - coordinate of $B'$: $y_{B'}=-2-4=-6$.
So the image of $B$ is $B'(11,-6)$.

Answer:

B. $B'(11,-6)$