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

If a point $(x,y)$ is dilated by a scale - factor $k$ about the origin, the new coordinates $(x',y')$ are given by $(x',y')=(k\cdot x,k\cdot y)$.

Step2: Identify coordinates of point A

Assume the coordinates of point A are $(x,y)$ (from the graph, if we can identify them, say $A=(1, - 1)$ for example).

Step3: Apply dilation formula

Since $k = 4$, if $A=(x,y)=(1,-1)$, then $A'=(4\times1,4\times(-1))=(4,-4)$. (We need to actually read the coordinates of A from the graph accurately. Let's assume we have read the coordinates of A as $(x_0,y_0)$). The coordinates of $A'$ will be $(4x_0,4y_0)$).

Answer:

(The coordinates of $A'$ are obtained by multiplying the coordinates of A by 4. Without seeing the exact coordinates of A on the graph, we can't give a specific numerical answer. But if the coordinates of A are $(a,b)$, the coordinates of $A'$ are $(4a,4b)$)