Question

draw the image of \\(\delta abc\\) under a dilation whose center is \\(p\\) and scale factor is 4.

Explanation:

Identify the coordinates of the center and vertices

$$
LATEXBLOCK0
$$

Apply the dilation formula with scale factor 4

$$
LATEXBLOCK1
$$

Verify the side lengths of the dilated triangle

$$
LATEXBLOCK2
$$

Answer:

To draw the image of \(\Delta ABC\) under a dilation centered at \(P\) with a scale factor of \(4\), multiply the vector from \(P\) to each vertex by \(4\):

• \(A'\) is located along the ray \(PA\), at a distance \(4 \times 1.0 = 4.0\) units to the right of \(P\).
• \(B'\) is located along the ray \(PB\), at a distance \(4 \times 2.0 = 8.0\) units to the left of \(P\).
• \(C'\) is located along the ray \(PC\), with coordinates scaled by \(4\) relative to \(P\).

The vertices of the dilated triangle \(\Delta A'B'C'\) relative to \(P(0,0)\) are:

$$
LATEXBLOCK0
$$