Question

draw the image of \\(\delta abc\\) under a dilation whose center is \\(p\\) and scale factor is 2.

Explanation:

Identify coordinates of the center and vertices

$$
LATEXBLOCK0
$$

Apply dilation formula with scale factor 2

$$
LATEXBLOCK1
$$

Verify the dilated image coordinates

$$
LATEXBLOCK2
$$

Answer:

To draw the image of \(\triangle ABC\) under a dilation centered at \(P\) with a scale factor of \(2\), multiply the vector from \(P\) to each vertex by \(2\):

• \(A'\) is located along the ray \(PA\) such that \(PA' = 2 \cdot PA\).
• \(B'\) is located along the ray \(PB\) such that \(PB' = 2 \cdot PB\).
• \(C'\) is located along the ray \(PC\) such that \(PC' = 2 \cdot PC\).

Using \(P\) as the origin \((0,0)\):

• \(A' = (6, 2)\)
• \(B' = (-6, 4)\)
• \(C' = (0, -4)\)