Question

Triangle JKL has vertices J(3,1),K(7,-5), and L(5,7). Determine the coordinates of the vertex L^(`) after the triangle is rotated by 180degrees clockwise about the origin.

Answer 1

(-5, -7)

Explanation:

To rotate a point (x,y) by 180 degrees about the origin, we can multiply its coordinates by the matrix:

-1 0

0 -1

So, to rotate the triangle JKL by 180 degrees about the origin, we can apply this transformation to each of its vertices. We have:

J(3,1) -> J^`(−3,−1)

K(7,−5) -> K^`(−7,5)

L(5,7) -> L^`(−5,−7)

Therefore, the coordinates of the vertex L^(`) after the triangle is rotated by 180 degrees clockwise about the origin are (-5, -7).