Question

Figure ABCD is transformed to figure A′B′C′D′:

A coordinate grid is labeled from negative 5 to 0 to 5 on both x and y axes at increments of 1. Figure ABCD has A at ordered pair 1, 1, B at 3, 3, C at 4, 2, D at 4, 1. Figure A prime B prime C prime D prime has A prime at ordered pair 1, negative 3, B prime at 3, negative 1, C prime at 4, negative 2, D at 4, negative 3.

Which angle in Figure A′B′C′D′ is equal to Angle CDA.?

Angle D prime A prime B prime.
Angle A prime B prime C prime.
Angle B prime C prime D prime.
Angle C prime D prime A prime.

Answer 1

Angle C prime D prime A prime

Answer 2

The correct option is 4.

Explanation:

It is given that figure ABCD is transformed to figure A′B′C′D′.

The vertices of ABCD are A(1,1), B(3,3), C(4,2) and D(4,1).

The vertices of A'B'C'D' are A'(1,-3), B'(3,-1), C'(4,-2) and D'(4,-3).

It is clear that the figure translate 4 units down and the rule of translation is

`(x,y)\rightarrow (x,y-4)`

Translation is a rigid transformation, it means image and preimge are congruent.

Since ABCD is translate 4 units down to make A′B′C′D′, therefore

`ABCD\cong A'B'C'D'`

Congruent part of congruent figures are congruent.

`\angle CDA\cong \angle C'D'A'`

Therefore the correct option is 4.