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.
Creating a Reflection
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.
- 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