is a parallelogram with , and . If the area of the parallelogram is , what is the value of ?

Source: NCTM Mathematics Teacher, November 2006

**SOLUTION**

**
**Draw a perpendicular to . If the x-coordinate of equals , its y-coordinate equals because has a slope of .

Use distance formula to calculate

Area of

Since is perpendicular to , its slope equals

Use distance formula to calculate

Squaring both sides

Substitute the value of from Eq.

Substitute the value of into Eq.

**Answer**:

**Alternative solution
**

We can find the coordinates of by adding the x-coordinate of and and the y-coordinates of and

Area of =area of rectangle -area of the four triangles , and

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