Question

What is the final position of point A(7,8) after the a translation of two units left one unit down and followed by 180 degrees clockwise rotation around the origin

Answer 1

To find the final position of point A(7,8) after a translation of two units left and one unit down, we subtract 2 from the x-coordinate and subtract 1 from the y-coordinate:
Translation: A(7-2, 8-1) = A(5, 7)

Next, to perform a 180 degrees clockwise rotation around the origin, we multiply the coordinates of point A by the matrix:
[cos(180), -sin(180)]
[sin(180), cos(180)]

The cosine of 180 degrees is -1, and the sine of 180 degrees is 0. Applying the matrix multiplication:

A'(x, y) = [5(-1) + 7(0), 5(0) + 7(-1)]
= [-5, -7]

Therefore, the final position of point A after the translation and rotation is A'(-5, -7).