Question

Square ABCD was translated using the rule (x. y) «-4,y + 15) to form A'B'CD. What are the coordinates of point

D in the pre-image if the coordinates of point D' in the image are (9, -8)?
TE
O (13, -23)
(5, 7)
O (18, 1)
O (6,4)

Answer 1

`(13,-23)`

Explanation:

Given

Translation:
`(x,y) -> (x-4,y+15)`

Required

Determine the pre-image of (9,-8)

In (9,8)

`x = 9` and
`y = -8`

So:

`(x,y) -> (x-4,y+15)`

Becomes

`(9,8) ->(x-4,y+15)`

By comparison:

`x - 4 = 9`

`y + 15 = 8`

Solving for (x):

`x - 4 = 9`

`x = 9 + 4`

`x = 13`

Solving for (y):

`y + 15 = -8`

`y = -8 - 15`

`y = -23`

Hence, the pre -image has a coordinate of
`(13,-23)`