Question

point (7, - 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 (3, 2)

Explanation:

Step1: Find translation vector

Let the translation vector be $(x,y)$. Given that point $P(-2,3)$ is translated to $(7, - 4)$. We find the change in $x$ - coordinate and $y$ - coordinate. The change in $x$ - coordinate is $7-(-2)=9$, and the change in $y$ - coordinate is $-4 - 3=-7$. So the translation vector is $(9,-7)$.

Step2: Apply translation to new point

We want to find the image of the point $(5,-1)$ under the same translation. Add the components of the translation vector to the coordinates of the point $(5,-1)$. The new $x$ - coordinate is $5 + 9=14$, and the new $y$ - coordinate is $-1+( - 7)=-8$.

Answer:

$(14,-8)$