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

Answer:

(c)

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