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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.

651 Views

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

1495 Views

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)

542 Views

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.

Let the point A(x, y) divide the line segment joining the points P(3, 3) and Q(6, - 6) in the ratio 1 : 2. Then,

Now, the co-ordinates of P are given as

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Here, we have, x₁ = 3, y₁ = 3;
x₂ = 6, y₂ = -6
So, co-ordinate of A be,

$equals space straight A space open square brackets fraction numerator 1 cross times 6 plus 2 cross times 3 over denominator 1 plus 2 end fraction comma space fraction numerator 1 cross times left parenthesis negative 6 right parenthesis plus 2 space straight x space 3 over denominator 1 plus 2 end fraction close square brackets equals space straight A space open square brackets fraction numerator 6 plus 6 over denominator 3 end fraction comma space fraction numerator negative 6 plus 6 over denominator 3 end fraction close square brackets equals straight A open square brackets 4 comma space 0 close square brackets$

∴ The point A is (4, 0) which lies on the line
2x + y + k = 0
⇒ 2(4) + 0 + k = 0
⇒ k = - 8. Ans.
Problems Based on Area of Triangle

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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).

83 Views

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

922 Views

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

2842 Views