2. The set of all points that forms a triangle of area 15 sq. units with the points (1,-2) and (-5, 3) lies on
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Answer:
left side of the triangle
The set of all points that forms a triangle of area 15 sq units with the points (1, -2) and (-5, 3) lies on.
solution : let a point (x, y) forms a triangle by joining the lines with (1, -2) and (-5, 3).
area of triangle = 1/2|x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)|
⇒15 = 1/2|x(-2 - 3) + 1(3 - y) - 5(y + 2)|
⇒30 = |-5x + 3 - y - 5y - 10|
⇒30 = |-5x - 6y - 7|
⇒30 = -5x - 6y - 7 or, -30 = -5x - 6y - 7
⇒5x + 6y + 37 = 0 or, 5x + 6y - 23 = 0
Therefore the set of all points will be (5x + 6y + 37)(5x + 6y - 23) = 0
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