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Coordinate Geometry

Short Answer Type

231. Find a relation between x and y if the points (x, y); (1, 2) and (7, 0) are collinear.

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232. Find a relation between x and y if the points (2, 1), (x, y) and (7, 5) are collinear.

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

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

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

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

We know that, ar (∆ABC)

equals 1 half left square bracket x subscript 1 left parenthesis y subscript 2 minus y subscript 3 right parenthesis plus x subscript 2 left parenthesis y subscript 3 minus y subscript 1 right parenthesis plus x open parentheses y subscript 1 minus y subscript 2 close parentheses right square bracket

Here, we have
x₁ = 3, y₁ = 0
x₂ = 4, y₂ = 5
and x₃ = -1, y₃ = 4
Now, area of ∆ABD

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Here,
 Now, area of rhombus (ABCD)
= 2 × ar (∆ABC)
= 2 × 12 = 24 Sq. units.