Question

The endpoints of line segment TD are T (3,6) and D (-2,4). Find the coordinates of the image after a reflection over the x-axis followed by a dilation with a scale factor: k = 2.

a) Reflect over the y-axis followed by a dilation with a scale factor k = 2.
b) Reflect over the x-axis followed by a dilation with a scale factor k = 2.
c) Reflect over the y-axis followed by a dilation with a scale factor k = 3.
d) Reflect over the x-axis followed by a dilation with a scale factor k = 3.

Answer 1

To find the coordinates of the image after a reflection over the x-axis followed by a dilation with a scale factor k = 2, reflect the coordinates over the x-axis and then apply the dilation.

Step-by-step explanation:

To find the coordinates of the image after a reflection over the x-axis followed by a dilation with a scale factor k = 2, we can follow these steps:

1. Reflect the coordinates over the x-axis by changing the sign of the y-coordinate. For point T (3,6), the reflected point is T' (3,-6), and for point D (-2,4), the reflected point is D' (-2,-4).
2. Next, apply the dilation by multiplying both coordinates of the reflected points by the scale factor k. Since k = 2, the new coordinates are T'' (3*-2, -6*2) = T'' (-6, -12) and D'' (-2*-2, -4*2) = D'' (4, -8).

Therefore, the coordinates of the image after a reflection over the x-axis followed by a dilation with a scale factor k = 2 are T'' (-6, -12) and D'' (4, -8).