Question

e illustration, line m is perpendicular to line n, and line r is perpendicular to line
select all that apply.
a. rotate figure i 180° around point p.
b. reflect figure i across line s.
c. reflect figure i across line m, and then reflect the image across line
d. reflect figure i across line n, and then rotate the image 90°
counterclockwise around point p.
kes a conjecture that figure i is congruent to figure ii. select each
e. rotate figure i 90° clockwise around point p, and then reflect the
ation or combination of transformations that can help della prove her
across line n.
f. rotate figure i 180° around point p, and then reflect the image a
r.

Explanation:

Step1: Analyze option A

A \(180^{\circ}\) rotation around point \(P\) is a rigid transformation. Rigid transformations preserve congruence.

Step2: Analyze option B

A reflection across line \(s\) is a rigid transformation. Rigid transformations preserve congruence.

Step3: Analyze option C

A double - reflection (across \(m\) then \(n\)) is equivalent to a rotation. Since \(m\perp n\), a double - reflection across perpendicular lines is a \(180^{\circ}\) rotation (a rigid transformation).

Step4: Analyze option D

A reflection across \(n\) (rigid) followed by a \(90^{\circ}\) counter - clockwise rotation (rigid) is a composition of rigid transformations.

Step5: Analyze option E

A \(90^{\circ}\) clockwise rotation (rigid) followed by a reflection across \(n\) (rigid) is a composition of rigid transformations.

Step6: Analyze option F

A \(180^{\circ}\) rotation (rigid) followed by a reflection (rigid) is a composition of rigid transformations.

Answer:

A. Rotate figure I \(180^{\circ}\) around point \(P\).
B. Reflect figure I across line \(s\).
C. Reflect figure I across line \(m\), and then reflect the image across line \(n\).
D. Reflect figure I across line \(n\), and then rotate the image \(90^{\circ}\) counterclockwise around point \(P\).
E. Rotate figure I \(90^{\circ}\) clockwise around point \(P\), and then reflect the image across line \(n\).
F. Rotate figure I \(180^{\circ}\) around point \(P\), and then reflect the image across line \(r\).