Question

The vertices of a triangle are as follows: (6, -3), (1, 5), and (8, -4). If you dilate the triangle by a scale factor of 3, what are the vertices of the new triangle?

1) (9, 0), (4, 8), (11, -1)
2) (9, -6), (4, 2), (11, -7)
3) (3, -6), (-2, 2), (5, -7)
4) (18, -9), (3, 15), (24, -12)

Answer 1

The vertices of the new triangle after a dilation by a scale factor of 3 are (18, -9), (3, 15), and (24, -12).

Step-by-step explanation:

To dilate a triangle by a scale factor of 3, we need to multiply the coordinates of each vertex by the scale factor. Let's apply this to each vertex of the original triangle:

• (6, -3) multiplied by 3 is (18, -9)
• (1, 5) multiplied by 3 is (3, 15)
• (8, -4) multiplied by 3 is (24, -12)

Therefore, the vertices of the new triangle after dilation are (18, -9), (3, 15), and (24, -12). This process magnifies the triangle's size while maintaining its proportional relationships, expanding each coordinate point by a factor of 3 along both axes and establishing the updated vertex locations within the dilated triangle.