The red figure is the transformed image of the blue figure. Gloria correctly identifies a single transformation that can move the blue figure onto the red figure.

Layla correctly identifies a sequence of two transformations that can be used.

Use the drop-down menus below to complete the statements describing the transformations they used.

Math item stem image
CLEAR CHECK
Gloria's Transformation

The blue image is
rotated 180° around the origin
.

Layla's Transformation

First, the blue image is
rotated 180° around the origin
.

Then, it is
reflected across the line y = x
.

the answer is b.

64

step-by-step explanation:

c=2πr=2·π·8≈64

1. 180°. the sum of the interior angles of a triangle is 180°, for the equilateral triangle that it has three equals side is 60°+60°+60°=180°.

2. 60°. each interior angle of a equilateral triangle is 60°

3. 120°. the measure of ∠m is 120°, the sum of the angles ∠m and ∠n is equal to 180°. so, in order to find the measure of ∠m, we have ∠m+∠n=180° > ∠m=180°-∠n > ∠m=180°-60°=120°.

4. 360°. the sum of the exterior angles of an equilateral triangle is ∠m+∠r+∠x=120°+120°+120°=360°. the exterior angles of any triangle always add 360°.

it is impossible.