Question

drag the blue points to create the image of the triangle under a dilation about the origin with a scale factor of 4.

Explanation:

Step1: Recall dilation rule

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

Step2: Identify triangle vertices

Let the vertices of the original triangle be $A(- 3,1)$, $B(-3, - 2)$, $C(1,-2)$.

Step3: Calculate new vertices

For vertex $A(-3,1)$ with $k = 4$, $A'=(4\times(-3),4\times1)=(-12,4)$.
For vertex $B(-3,-2)$ with $k = 4$, $B'=(4\times(-3),4\times(-2))=(-12,-8)$.
For vertex $C(1,-2)$ with $k = 4$, $C'=(4\times1,4\times(-2))=(4,-8)$.

Answer:

The new vertices of the dilated triangle are $(-12,4)$, $(-12,-8)$, and $(4,-8)$.