Question

A triangle in the first quadrant of the coordinate plane has vertices A (0,0). B 2,0), and C (0,3). If the triangle is dilated by a factor of 3, with point of Citation, what are the new vertices?

Answer 1

The dilation transformation by a factor of 3 with point A as the center of dilation results in the new vertices A (0,0), B (6,0), and C (0,9) for the triangle on the coordinate plane.

Step-by-step explanation:

The student is asking about the results of a dilation transformation on a triangle with vertices A (0,0), B (2,0), and C (0,3) on a coordinate plane when the triangle is dilated by a factor of 3 with point A as the center of dilation. To find the new vertices after dilation, we simply multiply the x and y coordinates of each vertex (except for point A, which will remain at the origin) by the dilation factor of 3. The calculations are as follows:

• For vertex A (0,0), it will stay the same, since multiplying by any factor will result in (0,0).
• For vertex B(2,0), the new position after dilation will be (2*3, 0*3) = (6,0).
• For vertex C(0,3), the new position after dilation will be (0*3, 3*3) = (0,9).

Therefore, the new vertices of the triangle after dilation will be A (0,0), B (6,0), and C (0,9).