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Coordinate Geometry

Short Answer Type

171.

The coordinates of the vertices of ∆ABC are A(4, 1), B(-3, 2) and C(0, k). Given that the area of ABC is 12 unit², find the value of k.

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172. Find the area of the ∆ABC with vertices A(-5, 7), B(-4, -5), and C(4, 5).

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173. For what value of k are the points (1, 1), (3, k) and (-1, 4) collinear.

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174. For what value of p are the points (2, 1), (p, -1) and (-1, 3) collinear.

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175. Find the area of the rhombus whose vertices taken in order are the points (3, 0), (4, 5), (-1, 4) and (-2, -1).

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176. Find the distance between the points
(cos ө - sin ө), (-cos ө, sin ө)

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177. Find the distance between the points
Let the given points be A (a cos ө, 0) and B(0, a sin ө)

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178. Find the distance between the points
Let the given points be A(0, 0) and B(6, 8) we know that distance between two points A(x₁, y₁) and B(x₂, y₂) is given by

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179. Find the co-ordinates of the mid-point of the line segment joining (-5, 4) and (6, -7).

Let the given points be A(-5, 4) and B(7, -8).
Here, we have
x₁ = -5, y₁ = 4
x₂ = 6, y₂ = -7
Let the co-ordinate of mid-point be P(x, y).

$Then comma space space straight x space equals space fraction numerator straight x subscript 1 plus straight x subscript 2 over denominator 2 end fraction space space and space straight y equals fraction numerator straight y subscript 1 plus straight y subscript 2 over denominator 2 end fraction rightwards double arrow space space straight x space equals fraction numerator negative 5 plus 6 over denominator 2 end fraction space space and space straight y space space equals fraction numerator 4 minus 7 over denominator 2 end fraction rightwards double arrow space space straight x equals 1 half space and space straight y space equals space fraction numerator negative 3 over denominator 2 end fraction therefore space space The space required space point space is space straight P open parentheses 1 half comma space fraction numerator negative 3 over denominator 2 end fraction close parentheses$

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180. Find the co-ordinates of the mid-point of the line segment joining (4, 7) and (6, 9).

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