Question:
if the vertices of a triangle are 1 -3 4 p and -9 7 and its area is 15 sq.units find the values of p
Answer:
Given, vertices of a triangle are (1, -3), (4, p) and (-9, 7)
and area of triangle is 15 sq.units
=> (1/2) * [1(p - 7) + 4(7 + 3) - 9(-3 - p)] = 15
=> 1(p - 7) + 4(7 + 3) - 9(-3 - p) = 15 * 2
=> p - 7 + 4 * 10 + 27 + 9p = 30
=> 10p - 7 + 40 + 27 = 30
=> 10p - 7 + 67 = 30
=> 10p + 60 = 30
=> 10p = 30 - 60
=> 10p = -30
=> p = -30/10
=> p = -3
So, the value of p is -3
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