Triangle ABC has vertices point A (2, 1), point B (4, 3), and point C (-2, 5). Find the coordinates of A, B, and C after a dilation with a scale factor of 7 and a center point of dilation at the origin (0, 0).
To find the new coordinates of each point after the dilation, we can multiply the original coordinates by the scale factor.
The new coordinates of point A are:
x-coordinate: 2 * 7 = 14
y-coordinate: 1 * 7 = 7
So, the new coordinates of point A are (14, 7).
The new coordinates of point B are:
x-coordinate: 4 * 7 = 28
y-coordinate: 3 * 7 = 21
So, the new coordinates of point B are (28, 21).
The new coordinates of point C are:
x-coordinate: -2 * 7 = -14
y-coordinate: 5 * 7 = 35
So, the new coordinates of point C are (-14, 35).
Therefore, after the dilation with a scale factor of 7 and a center point of dilation at the origin, the new coordinates of points A, B, and C are (14, 7), (28, 21), and (-14, 35), respectively.