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Contents
Examples
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Examples
 Example:  In
the quadrilateral PQRS, the points P, Q and S are as given in the diagram. The
line QS bisects the line PR at right angles at the point M. Find the equation
of QS and PR.
Calculate
(i)
the coordinates of M
(ii)
the coordinates of R
(iii)
the area of PQRS.
Solution:Gradient
of QS = (6-3)/6 = 1/2
Eqn
of QS : y - 3 = 1/2x
2y = x + 6 .....(1)
Gradient
of PR =
-2
perpendicular to QS
Eqn
of PR : y - 7 = -2 (x - 3)
y = -2x + 13 .....(2)
(i)
Solving (1) and (2) simultaneously,
x = 4, y = 5
The coordinates are (4, 5)
(ii)
Let the coordinates of R be (a, b).
([a+3]/2, [b+7]/2) = (4,
5) midpoint
formula
a + 3 = 8 --> a = 5
b + 7 = 10 --> b = 3
The coordinates are (5, 3)
(iii)
Area of quadrilateral
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