Question

dilate the triangle using center (0,0) and scale factor 2.

Explanation:

Step1: Identify original vertices

The original triangle has vertices $(0,0)$, $(2,0)$ and $(2,1)$.

Step2: Apply dilation formula

To dilate a point $(x,y)$ with center $(0,0)$ and scale - factor $k$, we use the formula $(x',y')=(k\cdot x,k\cdot y)$.
For vertex $(0,0)$: $(x',y') = 2\times(0,0)=(0,0)$.
For vertex $(2,0)$: $(x',y')=2\times(2,0)=(4,0)$.
For vertex $(2,1)$: $(x',y')=2\times(2,1)=(4,2)$.

Answer:

The new vertices of the dilated triangle are $(0,0)$, $(4,0)$ and $(4,2)$.