Question

Parallelogram JKLM is shown on the coordinate plane below:

Parallelogram JKLM with ordered pairs at J negative 6, 2, at K negative 4, 6, at L negative 3, 3, at M negative 5, negative 1.

If parallelogram JKLM is rotated 270° clockwise around the origin, what are the coordinates of the endpoints of the side congruent to side JM in the image parallelogram?

J′(−2, −6); M′(1, −5)
J′(6, 2); M′(−5, 1)
J′(2, 6); M′(−1, 5)
J′(6, −2); M′(5, 1)

Answer 1

After rotating parallelogram JKLM 270° clockwise around the origin, the coordinates of the endpoints of the side congruent to side JM are J'(-2, -6) and M'(1, -5).

Step-by-step explanation:

The problem involves the 270° clockwise rotation of parallelogram JKLM around the origin in a coordinate plane. To find the new coordinates of the endpoints of the side congruent to side JM after rotation, we need to apply a rotation transformation. Specifically, a 270° clockwise rotation around the origin will swap the x- and y-coordinates of each point and negate the new y-coordinate (or equivalently, negate the new x-coordinate for a counterclockwise rotation).

Applying this to points J and M:

• J(-6, 2) becomes J'(-2, -6) after rotation.
• M(-5, -1) becomes M'(1, -5) after rotation.

A quick check of the given options reveals that J'(-2, -6); M'(1, -5) matches our transformed coordinates. Therefore, the coordinates of the endpoints of the side congruent to side JM in the image parallelogram are J'(-2, -6); M'(1, -5).