Question

Lena reflected this figure across the x-axis. She writes the vertices of the image as A'(-2,8), B'(-5,6), C'(-8, 8), D'(-4,2). Lena is incorrect because

A) she reflected the pre-image across the y-axis.
B) she reflected the pre-image across the line y = x.
C) she rotated the pre-image 90 degrees counterclockwise.
D) she rotated the pre-image 180 degrees counterclockwise​

Answer 1

A) Lena reflected the pre-image across the y-axis.

Explanation:

Step 1:

As all the coordinates of the pre-image have negative x coordinates and positive y coordinates, the pre-image is on the second quadrant.

If we reflect an image across an axis, the coordinate values remain the same but the symbols vary according to the quadrant to which they are reflected.

If the pre-image was reflected across the x-axis, it would be in the third quadrant where both x and y coordinates have negative symbols.

Step 2:

The coordinates of the shape ABCD are A (2, 8), B (5, 6), C(8, 8), D (4, 2). All the coordinates have positive x and y coordinate values.

Only the first quadrant has such coordinates.

So Lena reflected the pre-image across the y-axis instead of the x-axis.