Question

The image of (-2, 5) is (1, 1).
What is the image of (3, 2) under the same translation?
(0, -2)
(3, -4)
(6, -2)
(7, 0)

Answer 1

Find the difference between A and A' to know the translation:

If the x coordinate goes from -2 to 1 then it moves a total distance of +3 in the x direction.
If the y coordinate goes from 5 to 1 then A moves a total distance of -4 in the y direction.
So the translation is (+3,-4)

Add the x coordinate of B to the x coordinate of translation: 3+3=6 in x direction
Add the y coordinate of B to the y coordinate of translation: 2-4=-2 in y direction
So under the same translation, B'(6,-2)..

Answer 2

Get the slope of the line, the line w.r.t (-2,5) is reflected.
\(\text{Note.}\) The slope would be perpendicular to the slope of line joining (-2,5) and (1,1).

Now that you have the slope (slope of (-2,5) and (1,1)) you can assume the image points for (3,2) as (x,y) and then equate it to the slope, which will give you an equation in two variables.


For the second equation, get the equation of the line (the line w.r.t the points are being reflected) in terms of x and y, you already have the slope but you need a point.
\(\text {Note.}\) The line must pass through ((x+3)/2,(y+2)/2).

You will get two equations now, solve them to get x and y.