I am asked to graph a triangle with the vertices (-3, 2), (5, 6), and (6, -4) after performing a dilation about the origin of scale factor 4.
What does "about the origin" mean? Is this the same as just multiplying the ordered pairs by 4? Are the new vertices (-12, 8), (20, 24), and (24, -16)?
you are correct.
A dilation might be around some other point, in which case distances to that point are scaled, and things get much more complicated.
"About the origin" refers to performing a dilation with the origin (0, 0) as the center point. When you are asked to perform a dilation about the origin, you need to multiply the coordinates of each vertex of the triangle by the scale factor.
To dilate a point (x, y) about the origin by a scale factor of 4, you multiply both the x-coordinate and the y-coordinate by 4.
So, let's apply this to the given vertices of the triangle:
- Vertex A (-3, 2): Multiply the x-coordinate (-3) and the y-coordinate (2) by 4: (-3 * 4, 2 * 4) = (-12, 8).
- Vertex B (5, 6): Multiply the x-coordinate (5) and the y-coordinate (6) by 4: (5 * 4, 6 * 4) = (20, 24).
- Vertex C (6, -4): Multiply the x-coordinate (6) and the y-coordinate (-4) by 4: (6 * 4, -4 * 4) = (24, -16).
So, after performing a dilation about the origin with a scale factor of 4, the new vertices of the triangle are (-12, 8), (20, 24), and (24, -16).