Answer:
- x = 6, y = 1, p = 7, q = 4
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Given figure is a parallelogram, since both pairs of opposite sides are parallel.
Property of a parallelogram:
- Diagonals bisect each other.
It means the intersection of diagonals is the midpoint of both diagonals.
Point (1, 3) is the midpoint of both AC and BD.
Use midpoint formula to find the unknown variables:
- [tex]x = \dfrac{x_1+x_2}{2}[/tex] and [tex]y = \dfrac{y_1+y_2}{2}[/tex]
Find x:
- (8 + x)/2 = 1
- 8 + x = 2
- x = 6
Find y:
- (5 + y)/2 = 3
- 5 + y = 6
- y = 1
Find p:
- (9 + p)/2 = 1
- 9 + p = 2
- p = 7
Find q:
- (2 + q)/2 = 3
- 2 + q = 6
- q = 4
