Please help me like i really don't understand this and i really need help

Therefore, the coordinates of the vertices of ΔA'B'C' after the dilation with a scale factor of 2.5.

Step-by-step explanation:

Given the vertices of ΔABC

Given that ΔA'B'C' is a dilation of ΔABC with a scale factor of 2.5 and the center of dilation (0, 0).

We know that when the scale factor > 1, then the image is enlarged.

The formula to determine the dilation with a scale factor of 2.5.

P(x, y) → P'(2.5x, 2.5y)

Here, P' is the image of P, and the vertices of the image is dilated by a scale factor of 2.5.

In other words, the vertices of the image can be obtained by multiplying the vertices of the original triangle with 2.5.

Thus,

P(x, y) → P'(2.5x, 2.5y)

A(-2, -1) → P'(2.5(-2), 2.5(-1)) = A'(-5, -2.5)

B(1, 2) → B'(2.5(1), 2.5(2)) = B'(2.5, 5)

C(2, -4) → C'(2.5(2), 2.5(-4)) = C'(5, -10)

Therefore, the coordinates of the vertices of ΔA'B'C' after the dilation with a scale factor of 2.5.