Question

1. dilate △abc on the coordinate plane using the origin (0, 0) as the center of dilation and a scale factor of 2

Explanation:

Step1: Identify the coordinates of the original triangle

Let's assume the coordinates of $\triangle ABC$ are $A(x_1,y_1)$, $B(x_2,y_2)$ and $C(x_3,y_3)$. From the graph, if we estimate: $A(2,1)$, $B(4,4)$, $C(4,2)$.

Step2: Apply the dilation formula

The formula for dilation with center at the origin $(0,0)$ and scale - factor $k$ is $(x,y)\to(kx,ky)$. Here $k = 2$.
For point $A(2,1)$: $(2\times2,2\times1)=(4,2)$
For point $B(4,4)$: $(2\times4,2\times4)=(8,8)$
For point $C(4,2)$: $(2\times4,2\times2)=(8,4)$

Step3: Plot the dilated triangle

The new triangle $\triangle A'B'C'$ with vertices $A'(4,2)$, $B'(8,8)$ and $C'(8,4)$ can be plotted on the same coordinate - plane.

Answer:

The vertices of the dilated $\triangle A'B'C'$ are $A'(4,2)$, $B'(8,8)$ and $C'(8,4)$