Question

dilations (module 2) quadrangle abcd is dilated by a scale factor of 4 about the origin to triangle abcd what are the coordinates of a?

Explanation:

Step1: Recall dilation rule

When dilating a point $(x,y)$ about the origin with a scale - factor $k$, the new coordinates $(x',y')$ are given by $(kx,ky)$.

Step2: Assume coordinates of A

Let the coordinates of point $A$ be $(x,y)$. Since the scale factor $k = 4$, the coordinates of $A'$ will be $(4x,4y)$. But we need to know the coordinates of $A$ from the graph. Suppose the coordinates of $A$ are $(1,1)$ (assuming from the context as no specific coordinates of $A$ are given in the text part, if we assume a sample point for illustration).
Then, $x'=4\times1 = 4$ and $y'=4\times1 = 4$.

Answer:

If the coordinates of $A$ are $(x,y)$, the coordinates of $A'$ are $(4x,4y)$. For example, if $A=(1,1)$, then $A'=(4,4)$.