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posted by Sandra on .
Determine whether parallelogram JKLM with vertices J(1, 1), K(4, 4), L(9, 1) and M(4, 6) is a rhombus, square, rectangle or all three.

First, plot the parallelogram on graphing paper. Next, calculate the length of each side using the formula for the distance between 2 points (x1, y1), (x2, y2):
((x1x2)^2 + (y1y2)^2)^0.5
Then calculate the slope of each line passing through these two points:
slope = (y2y1)/(x2x1)
If the angles are right angles, then the slopes of adjacent sides will be negative inverses of each other. If the slopes of adjacent sides are not negative inverses of each other, then the sides do not meet at right angles.
You should be able to use all this information to determine whether parallelogram JKLM is a rhombus, square, rectangle, or all three