Question

If translation T maps point A(-3, 1) onto point A'(5, 5),
which is the translation T?

Answer 1

Answer:
`(x,y) \to (x+8, y+4)`

==================================================

Step-by-step explanation:

The x coordinate of A and A' are -3 and 5 respectively.

This is an increase of +8 since -3+8 = 5

Therefore, we shift the preimage 8 units to the right to get the image point.

That explains how x turns into x+8.

-------------

The y coordinates of A and A' are 1 and 5 respectively.

This is an increase of +4, so we shift the preimage up 4 units.

This signals that y turns into y+4

--------------

To recap we found that,

• x becomes x+8
• y becomes y+4

Therefore we get to the answer
`(x,y) \to (x+8, y+4)`

--------------

To check the answer, let's apply this translation to point A(-3,1) and we should get (5,5) as the result.

`(\text{x},\text{y})\to(\text{x}+8,\text{y}+4)\\\\(-3,1)\to(-3+8,1+4)\\\\(-3,1)\to(5,5)\\\\`

This confirms the answer is correct.