Question

point p(-6, -4) is the image of point p(-2, 3) under a translation. what is the image of (5, -1) under the same translation?
a. (9, 6)
b. (1, -8)
c. (-1, -5)
d. (9, 2)

Explanation:

Step1: Find translation vector

Let the translation vector be $(a,b)$. Given point $P(- 2,3)$ is translated to $P'(-6,-4)$. So, $-2 + a=-6$ and $3 + b=-4$. Solving for $a$ and $b$, we get $a=-6+2=-4$ and $b=-4 - 3=-7$.

Step2: Apply translation to new point

We want to find the image of the point $(5,-1)$ under the same translation. The new $x$-coordinate is $5+a=5+( - 4)=1$, and the new $y$-coordinate is $-1 + b=-1+( - 7)=-8$.

Answer:

$(1,-8)$