Question

triangle abc is dilated using the origin as the center of dilation to create triangle abc. what rule best represents the dilation applied to triangle abc to create triangle abc? (x,y)→(4x,4y) (x,y)→(3x,3y) (x,y)→(1/2x,1/2y) (x,y)→(1/3x,1/3y)

Explanation:

Step1: Recall dilation rule

For a dilation with center at the origin $(0,0)$, the rule is $(x,y)\to(kx,ky)$ where $k$ is the scale - factor.

Step2: Determine scale - factor by comparing side lengths

Count the grid - units for corresponding sides of $\triangle ABC$ and $\triangle A'B'C'$. For example, if we consider a side of $\triangle ABC$ and its corresponding side of $\triangle A'B'C'$, we can see that the lengths of the sides of $\triangle A'B'C'$ are 4 times the lengths of the sides of $\triangle ABC$. So the scale - factor $k = 4$.

Answer:

A. $(x,y)\to(4x,4y)$