Select the coordinates A′ and B′ after dilation of the line segment AB with a scale factor of 13, centered at the origin where the endpoints are A(−6,3) and B(−12,9).

Question

A′(−18,9) and B′(−36,27)

A′(−6,3) and B′(−4,3)

A′(−2,1) and B′(−12,9)

A′(−2,1) and B′(−4,3)

Answer 1

To find the coordinates of A′ and B′ after the dilation, we can use the formula for dilation:

A′(x, y) = (h + k(x - h), k(y - k))

where (h, k) is the center of dilation and k is the scale factor.

In this case, the center of dilation is the origin (0, 0) and the scale factor is 13.

Let's find the coordinates of A′:
x = 0 + 13(-6 - 0) = -78
y = 0 + 13(3 - 0) = 39

So, A′ = (-78, 39)

Let's find the coordinates of B′:
x = 0 + 13(-12 - 0) = -156
y = 0 + 13(9 - 0) = 117

So, B′ = (-156, 117)

The correct answer is A′(-78,39) and B′(-156,117).