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) .
1.A′(−2,1) and B′(−12,9)
2.A′(−6,3) and B′(−4,3)
3.A′(−2,1) and B′(−4,3)
4.A′(−18,9) and B′(−36,27)
To perform a dilation with a scale factor of 13 centered at the origin, we can multiply the coordinates of each point by the scale factor.
For point A(-6, 3):
x-coordinate: -6 * 13 = -78
y-coordinate: 3 * 13 = 39
For point B(-12, 9):
x-coordinate: -12 * 13 = -156
y-coordinate: 9 * 13 = 117
The coordinates of A' and B' after dilation are:
A'(-78, 39)
B'(-156, 117)
Therefore, the correct answer is option 4. A'(-78, 39) and B'(-156, 117).