Question

Based on a graph below which sequence of transformation is needed to carry ABCD onto its image A’B’C’D?

Answer 1

Given:

The vertices of ABCD are A(2,3), B(5,6), C(8,6) and D(8,3).

The vertices of A'B'C'D' are A'(-2,6), B'(-5,3), C'(-8,3) and D'(-8,6).

To find:

The sequence of transformation is needed to carry ABCD onto its image A’B’C’D.

Solution:

The vertices of ABCD are A(2,3), B(5,6), C(8,6) and D(8,3).

If figure ABCD translated by the rule,
`(x,y)\to (x,y-9)`, then

`A(2,3)\to A_1(2,-6)`

`B(5,6)\to B_1(5,-3)`

`C(8,6)\to C_1(8,-3)`

`D(8,3)\to D_1(8,-6)`

Then the figure rotated 180 degrees clockwise about the origin. So,

`(x,y)\to (-x,-y)`

`A_1(2,-6)\to A'(-2,6)`

`B_1(5,-3)\to B'(-5,3)`

`C_1(8,-3)\to C'(-8,3)`

`D_1(8,-6)\to D'(-8,6)`

So, the required sequence of transformation that is needed to carry ABCD onto its image A’B’C’D is " A translation by the rule
`(x,y)\to (x,y-9)` and then a 180° clockwise rotation about the origin".

Therefore, the correct option is D.