Question

in the figure, p is the image of p under a reflection.
(a) find the axis of the reflection.
(b) find the image of p under the reflection.

(a) choose the correct graph below.

(b) choose the correct graph below.

Explanation:

Find the axis of reflection

The axis of reflection is the perpendicular bisector of the segment connecting point \(P\) and its image \(P'\).
Looking at the grid:

• Point \(P\) is located at \((0, 2)\) relative to a central origin, or we can count grid units.
• From \(P\) to \(P'\), the horizontal displacement is \(3\) units right, and the vertical displacement is \(3\) units down.
• The midpoint of \(PP'\) lies on the diagonal.
• The perpendicular bisector of a line segment with slope \(-1\) is a line with slope \(1\).
• Graph B shows the correct perpendicular bisector passing midway between \(P\) and \(P'\) at a \(45^\circ\) angle (slope \(1\)).

Find the image of P' under the reflection

A reflection is its own inverse (an involution).
Reflecting the image \(P'\) across the same axis of reflection maps it back to the original point \(P\).
Graph C shows the original point \(P\) highlighted as the final image of \(P'\) after reflection.

Answer:

Question 1

• A.
• B. (Correct answer)
• C.
• D.

Question 2

• A.
• B.
• C. (Correct answer)
• D.