Question

directions - dilate △abc by a scale factor of 4, centered at the origin: click to select polygon abc

Explanation:

Step1: Recall dilation formula

If a point $(x,y)$ is dilated by a scale - factor $k$ centered at the origin, the new point $(x',y')$ is given by $(x',y')=(kx,ky)$.

Step2: Identify coordinates of $\triangle ABC$

Assume $A(x_1,y_1)$, $B(x_2,y_2)$, $C(x_3,y_3)$. From the graph, if $A(1,1)$, $B(2,1)$, $C(2,2)$.

Step3: Calculate new coordinates

For point $A$: $x_1' = 4\times1=4$, $y_1' = 4\times1 = 4$.
For point $B$: $x_2'=4\times2 = 8$, $y_2'=4\times1 = 4$.
For point $C$: $x_3'=4\times2 = 8$, $y_3'=4\times2 = 8$.

Answer:

The vertices of the dilated triangle $\triangle A'B'C'$ are $A'(4,4)$, $B'(8,4)$, $C'(8,8)$.