McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
3. Tests for Parallelograms
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Exercise 40 Page 502

Remember that in a parallelogram diagonals bisect each other.

(-2,-2) and (-3,1)

Practice makes perfect

Let's begin with plotting the given points in the coordinate plane. Since the point of intersection of diagonals, let's call it P, is not between the given vertices, let's call them A and B, the distance between these vertices is a side.

Recall that in a parallelogram diagonals bisect each other. This means that the distance between B and P is the same as the distance between P and the fourth vertex, D. Since we can see that PB is 3, the fourth vertex will be 3 units to the left from the point of intersection.

To find the third vertex, C, we will also use the fact that the distance between A and P is the same as the distance between P and C. To get to the point P from the point A, we need to move down by 3 units and then move 2 units left. Let's repeat these moves starting in point P.

Now, we have all four vertices of this parallelogram.

The remaining vertices are located in (-2,-2) and (-3,1).