ΔABC has coordinates of A (–5, –7), B (6, –3), and C (2, 7). Find the coordinates of its image after a dilation centered at the origin with a scale factor of 2.
A (–10, –14), B (12, –6), C (4, 14)
A (–10, –7), B (12, –3), C (4, 7)
A (–2.5, –3.5), B (3, –1.5), C (1, 3.5)
A (–5, –7), B (6, –3), C (2, 7)
The coordinates of point A after the dilation can be found by multiplying each coordinate of A by the scale factor of 2:
x-coordinate of A: -5 * 2 = -10
y-coordinate of A: -7 * 2 = -14
Therefore, the coordinates of point A after the dilation are (-10, -14).
Similarly, the coordinates of point B after the dilation can be found by multiplying each coordinate of B by the scale factor of 2:
x-coordinate of B: 6 * 2 = 12
y-coordinate of B: -3 * 2 = -6
Therefore, the coordinates of point B after the dilation are (12, -6).
Lastly, the coordinates of point C after the dilation can be found by multiplying each coordinate of C by the scale factor of 2:
x-coordinate of C: 2 * 2 = 4
y-coordinate of C: 7 * 2 = 14
Therefore, the coordinates of point C after the dilation are (4, 14).
So, the correct answer is option A: A (-10, -14), B (12, -6), C (4, 14).