Answer:
A(-9, -4.5), B(10.5, -10.5), and C(0, 4.5)
Explanation:
To find the coordinates of the image of triangle ABC after a dilation centered at the origin with a scale factor of 1.5, we need to multiply the coordinates of each point by 1.5.
The coordinates of point A after dilation can be found by multiplying its x-coordinate and y-coordinate by 1.5:
x-coordinate of A after dilation = 1.5 × (-6) = -9
y-coordinate of A after dilation = 1.5 × (-3) = -4.5
So the coordinates of point A after dilation are (-9, -4.5).
Similarly, we can find the coordinates of points B and C after dilation:
x-coordinate of B after dilation = 1.5 × 7 = 10.5
y-coordinate of B after dilation = 1.5 × (-7) = -10.5
Coordinates of point B after dilation are (10.5, -10.5).
x-coordinate of C after dilation = 1.5 × 0 = 0
y-coordinate of C after dilation = 1.5 × 3 = 4.5
Coordinates of point C after dilation are (0, 4.5).
Therefore, the coordinates of the image of triangle ABC after a dilation centered at the origin with a scale factor of 1.5 are:
A(-9, -4.5), B(10.5, -10.5), and C(0, 4.5)