Question

I really need help!

Angle PQR is formed by segments PQ and QR on the following coordinate grid:
Angle PQR is rotated 90 degrees counterclockwise about the origin to form angle P′Q′R′. Which statement shows the measure of angle P′Q′R′?
a. m∠P′Q′R′ = 90 degrees
b. m∠P′Q′R′ = 180 degrees
c. m∠P′Q′R′ = m∠PQR
d. m∠P′Q′R′ = 2 ⋅ m∠PQR

Answer 1

Option c is right

Explanation:

Rotation means turning around a centre. Here O, the origin is the centre. And angle PQR is rotated 90 degrees counter clockwise about the origin.

Rotation is the change of direction, but normally the sizes and angles will not change.

Here by rotation angle PQR will not change (neither increase or decrease)

Hence Angle PQR = angle P'Q'R' Option c is right

Option a is not right since the new angle need not be 90 degrees unless we know PQR =90

Similarly for b also it is wrong

d is wrong since rotation will not make angle 2 times.

Hence option c is right answer

Answer 2

c. m∠P'Q'R' = m∠PQR

Explanation:

Rotation is a rigid transformation. It does not change lengths or angles.