Check to see if all three properties of a reflection are met. 1. Example 1 Identify Reflections Tell whether the red triangle is the reflection of the blue triangle in line m. SOLUTION Check to see if all three properties of a reflection are met. 1. Is the image congruent to the original figure? Yes. 2. Is the orientation of the image reversed? Yes. ∆FGH has a clockwise orientation. ∆F'G'H' has a counter clockwise orientation. 3. Is m the perpendicular bisector of the segments connecting the corresponding points? Yes. 1

To check, draw a diagram and connect the corresponding endpoints. Example 1 Identify Reflections To check, draw a diagram and connect the corresponding endpoints. Because all three properties are met, the red triangle is the reflection of the blue triangle in line m. ANSWER 2

Check to see if all three properties of a reflection are met. SOLUTION Example 2 Identify Reflections Tell whether the red triangle is the reflection of the blue triangle in line m. Check to see if all three properties of a reflection are met. SOLUTION 1. Is the image congruent to the original figure? Yes. 2. Is the orientation of the image reversed? No. The red triangle is not a reflection of the blue triangle. ANSWER 3

Which segment is the reflection of AB in the x-axis? Which point Example 3 Reflections in a Coordinate Plane Which segment is the reflection of AB in the x-axis? Which point corresponds to A? to B? a. b. Which segment is the reflection of AB in the y-axis? Which point corresponds to A? to B? SOLUTION a. The x-axis is the perpendicular bisector of AJ and BK, so the reflection of AB in the x-axis is JK. A is reflected onto J. A(–4, 1) J(–4, –1) B is reflected onto K. B(–1, 3) K(–1, –3) 4

Example 3 Reflections in a Coordinate Plane Which segment is the reflection of AB in the y-axis? Which point corresponds to A? to B? b. The y-axis is the perpendicular bisector of AD and BE, so the reflection of AB in the y-axis is DE. A is reflected onto D. A(–4, 1) D(4, 1) B is reflected onto E. B(–1, 3) E(1, 3) 5

Checkpoint Identify Reflections Tell whether the red figure is a reflection of the blue figure. If the red figure is a reflection, name the line of reflection. 1. 2. 3. ANSWER yes; the x-axis ANSWER no ANSWER yes; the y-axis