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

Answers

Answered by GPT 3.5
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).
There are no human answers yet. A form for humans to post answers is coming very soon!

Related Questions