Question

your friend gave you the graph of abcd and the image abcd. what reflection produces the image abcd? use pencil and paper. draw the image of abcd using a reflection across a different line.

what reflection produces the image abcd?

a. abcd is the image of abcd after a reflection across the line y = -3.

b. abcd is the image of abcd after a reflection across the line x = -1.

c. abcd is the image of abcd after a reflection across the y - axis.

d. abcd is the image of abcd after a reflection across the x - axis.

Explanation:

To determine the reflection, we analyze the horizontal or vertical symmetry. The blue figure (ABCD) and red figure (A'B'C'D') are symmetric about the vertical line \( x = -1 \). Let's check the x - coordinates of corresponding points. For a vertical reflection over \( x = a \), the midpoint of a point \( (x,y) \) and its image \( (x',y) \) is \( x=\frac{x + x'}{2} \). By observing the grid, the vertical line of symmetry between the two figures is \( x=-1 \). Option A is about horizontal reflection (y - line), D is x - axis reflection (horizontal), C is y - axis (\( x = 0 \)) reflection. So the correct reflection is across \( x=-1 \).

Answer:

B. A'B'C'D' is the image of ABCD after a reflection across the line \( x=-1 \)