What is point A (6, 9) after a translation of 2 units left and 2 units down followed by a 180° clockwise rotation around the origin

Answer 1

After a translation of 2 units left and 2 units down, the new coordinates of point A would be (4, 7).

After a 180° clockwise rotation around the origin, the new coordinates (x', y') can be found using the following formulas:

x' = x * cos(theta) + y * sin(theta)
y' = -x * sin(theta) + y * cos(theta)

where theta is the angle of rotation (180° in this case).

Using these formulas, we can calculate the new coordinates after the rotation:

x' = 4 * cos(180°) + 7 * sin(180°) = 4 * (-1) + 7 * 0 = -4
y' = -4 * sin(180°) + 7 * cos(180°) = -4 * 0 + 7 * (-1) = -7

Therefore, point A (6, 9) after a translation of 2 units left and 2 units down followed by a 180° clockwise rotation around the origin is (-4, -7).