Question

Parallelogram JKLM is shown on the coordinate plane below:

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?

Answer 1

Given that rotating 90 degrees clockwise around the origin switches the x andy values and makes the new y value negative, we can, for example, switch (2, 1) to (1, -2). 180 degrees clockwise simply makes both values negative (-2, -1), and 270 degrees clockwise switches them and makes the new y value negative  (-1, 2), we can plug those in to our JM endpoints to turn (-5, 1) into (-1, -5) and (-6, 2) into (-2, -6)

Answer 2

The coordinates of the endpoints of the side congruent to side JM will be,

(-2, -6) and (1, -5).

Solution-

When rotating a point 270° clockwise or 90° counter-clockwise around the origin, we apply the rule (x, y) → (-y, x).

The co-ordinates of the original parallelogram are,

J = (-6, 2)

M = (-5, -1)

L = (-3, 3)

K = (-4, 6)

After the rotation, the new co-ordinates will be,

J = (-2, -6)

M = (1, -5)

L = (-3, -3)

K = (-6, 4)

∴ The coordinates of the endpoints of the side congruent to side JM will be,

(-2, -6) and (1, -5).