Question

If triangle K'L'M' represents triangle KIM rotated 180° about the origin, the ordered pair of M’ is:

a) (x, -y)
b) (-x, y)
c) (-x, -y)
d) (x, y)

Answer 1

The coordinates of point M' after a 180° rotation around the origin would be (-x, -y), meaning the correct answer to the student's question is option c).

Step-by-step explanation:

The question revolves around the topic of geometry, specifically the rotation of triangles on the coordinate plane. When a point or figure is rotated 180° around the origin, the coordinates of the point (x, y) become (-x, -y). This is because a 180° rotation is equivalent to reflecting a point over both the x-axis and y-axis.

Therefore, if triangle K'L'M' is a rotation of triangle KIM by 180° about the origin, and we want to find the coordinates of point M' after the rotation, we can apply this rule. Assuming the original coordinates of point M are (x, y), the coordinates of M' after a 180° rotation would be (-x, -y).