Question

Point A is located at coordinates (-4,3). у. А 2 1 -3 -2 2. 3 $ X 1 2 3 What are the coordinates of each point? 1. Point B is the image of A after a rotation of 180° using (0,0) as center. 2. Point C is the image of A after a translation two units to the right, then a reflection using the c-axis. 3. Point D is the image of A after a reflection using the y-axis, then a translation two units to the right.

Answer 1

1. The rotation of a point in 180 degrees is given by reflecting both of its coordinates. In this case the original point is (-4, 3), so the rotated point will be (4, -3).

2. When we reflect a point around the x-axis we need to invert the signal of the y-coordinate. When we make a translation to the right we need to add the number of units to the x-coordinate of the point, therefore.

Translation:

A' = (-4 + 2, 3) = (-2, 3)

Reflection x-axis:

C = (-2, -3)

3. When we reflect a point around the y-axis we invert the signal of x-coordinate. To perform a translation to the right we add the number of units to the x-coordinates, therefore:

Reflection y-axis:

A'' = (4, 3)

Translation:

D = (4 + 2, 3) = (6,3)