Question

Dilate the ∆ABC by a scale factor of `\frac{1}{2}` to create ∆A'B'C'

Answer 1

To dilate ΔABC by a scale factor of ½ to create ΔA'B'C', halve the original coordinates of ΔABC's vertices, preserving their orientation and relative positions.

Step-by-step explanation:

To dilate the ΔABC by a scale factor of ½, we transform each vertex of the triangle by multiplying its distance from the origin (in a coordinate system) by the scale factor. In this case, each vertex's coordinates A, B, and C will be halved, which means if the original coordinates for the triangle's vertices are (x1, y1), (x2, y2), and (x3, y3), after dilation the new vertices A', B', and C' will have the coordinates (½ * x1, ½ * y1), (½ * x2, ½ * y1), and (½ * x3, ½ * y3), respectively.

It is crucial to maintain the orientation and relative positions of the vertices after dilation to correctly form ΔA'B'C'.