Question

Triangle LMN has vertices at L(−1, 4), M(−1, 0), N(−3, 4) Determine the vertices of image L′M′N′ if the preimage is rotated 180° counterclockwise about the origin.

L′(4, 1), M′(0, 1), N′(4, 3)
L′(−1, −4), M′(−1, 0), N′(−3, −4)
L′(−4, −1), M′(0, −1), N′(−4, −3)
L′(1, −4), M′(1, 0), N′(3, −4)

Answer 1

Therefore, the vertices of the image L'M'N' after rotating the triangle 180° counterclockwise about the origin are:

L'(1, -4), M'(1, 0), N'(3, -4)

Explanation:

To determine the vertices of the image L'M'N' after rotating the triangle LMN 180° counterclockwise about the origin, we can apply the rotation transformation to each vertex.

The rotation of a point (x, y) by 180° counterclockwise about the origin can be obtained by switching the signs of both coordinates. So, if the original vertex is (x, y), the rotated vertex will be (-x, -y).

Applying this to each vertex:

L'(-x, -y) = L'(-(-1), -(4)) = L'(1, -4)

M'(-x, -y) = M'(-(-1), -(0)) = M'(1, 0)

N'(-x, -y) = N'(-(-3), -(4)) = N'(3, -4)

Therefore, the vertices of the image L'M'N' after rotating the triangle 180° counterclockwise about the origin are:

L'(1, -4), M'(1, 0), N'(3, -4)