Question

If the vertex H of a triangle is at (-2, 2), what are the coordinates of H´ in the dilation of the triangle when (-2, 1) is the center of dilation, and the scale factor is 5?

a) (-2, 6)
b) (-6, 5)
c) (1, 5)
d) (2, -2)

Answer 1

The dilation of vertex H at (-2, 2) centered at (-2, 1) with a scale factor of 5 results in the image H´ having coordinates (-2, 6), as the dilation affects only the distance to the center of dilation and in this case the y-coordinate.

Step-by-step explanation:

The given problem involves finding the coordinates of H´, which is the image of vertex H after a dilation centered at (-2, 1) with a scale factor of 5. To calculate the coordinates of H´ after the dilation, you need to apply the scale factor to the distance from the center of dilation to vertex H's coordinates.

The vertex H at (-2, 2) is 1 unit above the center of dilation at (-2, 1). With a scale factor of 5, this distance is multiplied by 5, making H´ now 5 units from the center of dilation instead of 1. Thus, since the center of dilation will not move in the y-axis, we just multiply the distance from the center to H by the scale factor. H´ is 5 × 1 = 5 units above the center of dilation. So if the center is at y-coordinate of 1, adding the 5 units we get 1 + 5 = 6 for the new y-coordinate. Since dilation wouldn't affect the x-coordinate of H because it lines up with the center of dilation, the x-coordinate remains unchanged.

Therefore, the correct answer for the coordinates of H´ is (-2, 6).