Question

the triangle pqr is rotated counterclockwise about the origin to form a triangle pqr.which statement is true?○ the measure of $overline{pq}$ is 7 centimeters.● the measure of $overline{pq}$ is 8 centimeters.○ the measure of $overline{pr}$ is 9 centimeters.○ the measure of $overline{qr}$ is 7 centimeters.

Explanation:

Rotation is a rigid transformation, meaning it preserves the lengths of all sides of the figure. So each side of triangle \(P'Q'R'\) has the same length as the corresponding side of triangle \(PQR\).

• \(PQ = 9\) cm, so \(P'Q' = 9\) cm
• \(PR = 8\) cm, so \(P'R' = 8\) cm
• \(QR = 7\) cm, so \(Q'R' = 7\) cm

Checking each option:

1. The measure of \(P'Q'\) is 7 cm: False (it is 9 cm)
2. The measure of \(P'Q'\) is 8 cm: False (it is 9 cm)
3. The measure of \(P'R'\) is 9 cm: False (it is 8 cm)
4. The measure of \(Q'R'\) is 7 cm: True (matches the preserved length)

Answer:

The measure of \(Q'R'\) is 7 centimeters.