Question

Triangle ABC is shown on the coordinate plane. Triangle on coordinate plane with vertices A at (8, 2), B at (10, 6), and C at (4, 4). Triangle ABC is dilated by a scale factor of one half about the origin and then reflected over the x-axis. What is the location of B' after the sequence of transformations?

1) (-10, 6)
2) (-5, 3)
3) (5, 3)
4) (5, -3)

Answer 1

The location of B' after the sequence of transformations is (5, -3).

Step-by-step explanation:

To find the location of B' after the sequence of transformations, we first need to perform the dilation by a scale factor of one-half about the origin. This means that each coordinate of B will be multiplied by 0.5. So, the new coordinates of B are (10 * 0.5, 6 * 0.5) = (5, 3).

Next, we need to reflect the triangle over the x-axis. This means that the y-coordinate of each vertex needs to be negated. So, the new coordinates of B' are (5, -3).

Therefore, the location of B' after the sequence of transformations is (5, -3).