# Reflections - Day 1

## Example 1 Draw the image of ABC after a reflection across line .

• Step 1 Draw a segment with an endpoint at vertex A so that the segment is perpendicular to line  and is bisected by line . Label the other endpoint of the segment A'.
• Step 2 Repeat Step 1 at vertices B and C.
• Step 3 Connect points A′, B′, and C′.△A′B′C′ is the image of △ABC.

## Draw the image of △ABC after a reflection across line ℓ.

• Step 1 Draw a segment with an endpoint at vertex A so that the segment is perpendicular to line ℓ and is bisected by line ℓ. Label the other endpoint of the segment A′.
• Step 2 Repeat Step 1 at vertex B.
Notice that C and C' are the same point because C is on the line of reflection.
• Step 3 Connect points A', B', and C'. △A'B'C' is the image of △ABC.

## Reflection 1

How can you check that you drew the image of the triangle correctly?

In Part A, how can you tell that line segment AA' is perpendicular to line ℓ?

## Your Turn: Draw the image of △ABC after a reflection across line ℓ

Reflect the figure with the given vertices across the given line.
• Step 1 Find the coordinates of the vertices of the image.
• M(1, 2), N(1, 4), P(3, 3); y-axis

A(x, y) A'(-x, y). M(1, 2) M'(-1, 2) N(1, 4) N'(-1, 4) P(3, 3) P'(-3, 3)

• Step 2 Graph the preimage.
• Step 3 Predict the quadrant in which the image will lie. Since MNP lies in Quadrant I and the triangle is reflected across the y-axis, the image will lie in Quadrant II.
• Graph the image.
Step 1 Find the coordinates of the vertices of the image.

A (x, y) A' ( ___ , ___ ) D (2, 0)  D' ( ___ , ___ ) E (2, 2)  E' ( ___ , ___ ) F (5, 2)  F'( ___ , ___ ) G (5, 1) G' ( ___ , ___ )

Step 2 Graph the preimage. Step 3 Since DEFG lies in Quadrant I and the quadrilateral is reflected across the line y = x, the image will lie in Quadrant _______. Graph the image.
Reflect the figure with the given vertices across the given line. S(3, 4), T(3, 1), U(−2, 1), V(−2, 4); x-axis
Reflect the figure with the given vertices across the given line. A(-4, -2), B(-1, -1), C(-1, -4); y = -x