Question

A triangle has vertices at O(0, 0), A(1, 0), and B(0, 1). A dilation centered at (1, 0) is applied to the triangle. Which of the sides lie on the same line as their respective images?

A. None
B. All three
C. One
D. Two

Answer 1

The sides OA, AB, and BO of the triangle lie on the same line as their respective images.

Step-by-step explanation:

A dilation centered at (1, 0) means that the original triangle is going to be expanded or contracted from the point (1, 0). To determine which sides lie on the same line as their respective images, we need to apply the dilation to each side of the triangle.

The first side, OA, will be expanded or contracted by the same factor as the dilation centered at (1, 0). Since point O is the center of dilation, this line will not move and will remain on the line y = 0. Therefore, side OA lies on the same line as its respective image.

The other two sides of the triangle, AB and BO, will be transformed by the dilation. However, they will still lie on the same line as their respective images. Side AB will be expanded or contracted along the line x = 1, which is the vertical line passing through (1, 0). Side BO will be expanded or contracted along the line x = 0, which is the y-axis. Therefore, both sides AB and BO lie on the same line as their respective images.