Question

Rectangle ABCD went through a transformation and is now rectangle A'B'C'D'. Explain two different ways how rectangle ABCD becomes rectangle A'B'C'D'.

Answer 1

(c)

Step-by-step explanation:

Given

See attachment for rectangles ABCD and A'B'C'D

Required

Determine two possible ways of transformation

From the attachment, we have:

ABCD coordinates:

`A = (-6,5)`

`B = (-1,5)`

`C = (-1,1)`

`D = (-6,1)`

A'B'C'D' coordinates:

`A' = (5,-1)`

`B' = (5,-6)`

`C' = (1,-6)`

`D' = (1,-1)`

The first transformation is a rotation of ABCD by 90 degrees using the rule:

(x,y) => (y,-x)

So, we have:

`A = (-6,5)` ===>
`(5,6)`

`B = (-1,5)` ===>
`(5,1)`

`C = (-1,1)` ===>
`(1,1)`

`D = (-6,1)` ===>
`(1,6)`

Next, is to translate 7 units down using the rule

(x,y) => (x,y-7)

So, we have:

`(5,6)` ==>
`(5,6-7)`

`(5,1)` ==>
`(5,1-7)`

`(1,1)` ==>
`(1,1-7)`

`(1,6)` ==>
`(1,6-7)`

This gives

`A' = (5,-1)`

`B' = (5,-6)`

`C' = (1,-6)`

`D' = (1,-1)`

Option (c) is correct