Question

Point AA is located at coordinates (-4, 3). Point A in an xy-plane. What are the coordinates of each point?

Point BB is the image of Point AA after a rotation of 180 degrees using (0,0) as the center. Point CC is the image of Point AA after a translation two units to the right, then a reflection using the x-axis. Point DD is the image of Point AA after a reflection using the y-axis, then a translation two units to the right.

a. BB: (-4, -3), CC: (-2, 3), DD: (4, 3)
b. BB: (4, -3), CC: (6, 3), DD: (-4, 3)
c. BB: (4, 3), CC: (6, 3), DD: (-4, -3)
d. BB: (-4, 3), CC: (-2, 3), DD: (4, -3)

Answer 1

Point B has coordinates (-4, -3), Point C has coordinates (-2, -3), and Point D has coordinates (6, 3).

Step-by-step explanation:

To find the coordinates of point B, we need to rotate point A by 180 degrees around the origin (0,0). This means that the x-coordinate of B will be the negative of the x-coordinate of A, and the y-coordinate of B will be the negative of the y-coordinate of A. Therefore, the coordinates of B will be (-(-4), -3), which simplifies to (-4, -3).

To find the coordinates of point C, we first translate point A two units to the right. This means we add 2 to the x-coordinate of A, so we get (-4 + 2, 3) which simplifies to (-2, 3). Then, we reflect point C using the x-axis, which means the y-coordinate of C will be the negative of its original y-coordinate. Therefore, the coordinates of C will be (-2, -3).

To find the coordinates of point D, we first reflect point A using the y-axis. This means the x-coordinate of D will be the negative of its original x-coordinate, so we get (-(-4), 3) which simplifies to (4, 3). Then, we translate point D two units to the right, which means we add 2 to the x-coordinate of D, so we get (4 + 2, 3) which simplifies to (6, 3).