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Coordinate Geometry

Short Answer Type

221. In what ratio does the like x - y - 2 = 0 divides the line segment joining (3, -1) and (8, 9) ?

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222. Find the ratio in which the point (x, -1) divides the line segment joining the points (-3, 5) and (2, -5). Also find the value of x

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223. Find the ratio in which the point (2, y) divides the line segment joining the points A(-2, 2) and B (3, 7). Also find the value of y.

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224. In what ratio does the point P(2, -5) divide the line segment joining A(-3, 5) and B (4, -9)?

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225. The mid-points of the sides of a triangle are (3, 4), (4, 6) and (5, 7). Find the coordinates of the vertices of the triangle.

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226. Determine the ratio in which the line 3x + 4y - 9 = 0 divides the line segment joining the points (1, 3) and (2, 7)

Let the given points arc A(1, 3) and B(2, 7). Let the line 3x + 4y - 9 = 0 divides the line segment AB in the ratio K : 1 at point P. Then the co-ordinates of P are given as

"<pre

Here, we have x₁ = 1,    y₁ = 3
x₂ = 2,    y₂ = 7
and    m₁ = k, m₂ = 1
So, co-ordinates of P are

equals straight P space open square brackets fraction numerator straight K cross times 2 plus 1 cross times 1 over denominator straight K plus 1 end fraction comma space fraction numerator straight K cross times 7 plus 1 cross times 3 over denominator straight K plus 1 end fraction close square brackets equals straight P space open square brackets fraction numerator 2 straight K plus 1 over denominator straight K plus 1 end fraction comma space fraction numerator 7 straight K plus 3 over denominator straight K plus 1 end fraction close square brackets

But P lies on 3x + 4y - 9 = 0 ...(i)
Substituting the values of x (abscissa) and y (ordinate) in (i), we get
3x + 4y - 9 = 0
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Hence, the required ratio is $space space space fraction numerator negative 6 over denominator 25 end fraction$ .

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227. A line segment joining the points P(3, 3) and Q(6, - 6) is trisected at the points A and B such that A is nearer to P. If A also lies on the line given by 2x + y + k = 0, find the value of k.

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228. Find the area of the quadrilateral w hose vertices are A(0, 0), B(6, 0), C(4, 3) and D(0, 3).

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229. Find the area of the quadrilateral whose vertices, taken in order are (-4, -2), (-3, -5), (3, -2) and (2, 3).

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230. Find the value of ‘K’ if the points (K, 3), (6, -2) and (-3, 4) are collinear.

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