Question

What is the image of (x,y) after a translation of 3 units left and 7 units down?

Answer 1

`(x + 3, y - 7)`

Explanation:

Given

`Function = (x,y)`

Translation:

`Left = 3\ units`

`Down = 7\ units`

Required

Determine the image of the function

Apply the first translation

`Left = 3\ units`

When function (x,y) is 3 units translated left, we add the units to the x value.

The new function becomes:

`(x,y) -> (x + 3, y)`

Apply the second translation

`Down = 7\ units`

We subtract 7 units from the y value

`(x,y) -> (x + 3, y)`

becomes:

`(x + 3, y) ->(x + 3, y - 7)`

Hence:

The image of the function is:

`(x + 3, y - 7)`