Question

The image of point (−3, 5) under translation T is (6, -8). What is the image of point (4, 7) under the same translation?

Answer 1

(13, -6)

Explanation:

Firstly, we need to find the translation. This can be achieved by calculating the amount the x and y coordinate shifts. Simply use the following equation:

`(x2 - x1, y2 - y1)`

Where x1 and y1 are the coordinates of the first set and x2 and y2 are the second. Plug the variables in:

`(6 - (-3), -8 - 5)\\(9, -13)`

So the x coordinate is shifted 9 positively and the y coordinate is shifted 13 negatively.

To calculate the new translation of the new point, add the translation onto the given coordinates:

`( 4 + 9, 7 + (-13) )\\(13, -6)`

So the new point is (13, -6).

Hope this helps!

Answer 2

(13,-6)

Explanation:

If you are at (-3,5) and you translate T to give you (6,-8), that means you translated (9,-13) because you moved right 9 units in the positive x direction and down 13 units in the negative y direction.

Apply this translation T to (4,7) and you get (13,-6).