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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)

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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).

Let the vertices of quadrilateral are A(-4, -2), B(-3, -5), C(3, -2) and D(2, 3).

Area of ∆ABC

equals 1 half left square bracket straight x subscript 1 left parenthesis straight y subscript 2 minus straight y subscript 3 right parenthesis plus straight x subscript 2 left parenthesis straight y subscript 3 minus straight y subscript 1 right parenthesis plus straight x subscript 3 left parenthesis straight y subscript 1 minus straight y subscript 2 right parenthesis right square bracket

Here, we have x₁ = -4, y₁ = -2
x₂ = -3, y₂ = -5
and x₃ = 3, y₃ = -2
Now. area of ∆ABC

$equals 1 half left square bracket negative 4 left parenthesis negative 5 plus 2 right parenthesis plus left parenthesis negative 3 right parenthesis left parenthesis negative 2 plus 2 right parenthesis plus 3 left parenthesis negative 2 plus 5 right parenthesis right square bracket equals 1 half left square bracket left parenthesis negative 4 space straight x space space minus 3 right parenthesis space plus space left parenthesis negative 3 space straight x space 0 right parenthesis plus left parenthesis 3 space straight x space 3 right parenthesis right square bracket equals 1 half left square bracket 12 plus 0 plus 9 right square bracket equals 1 half space straight x space 21 space equals space 10.5 space sq. space units.$

We know, area of ∆ACD

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Here, we have x₁ = -4,    y₁ = -2
x₂ = 3,    y₂ = -2
and    x₃ = 2, y₃ = 3
Now, area of ∆ACD

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Hence, the area of quadrilateral
ABCD = ar (∆ABC) + ar (∆ACD)
= (10.5 + 17.5) = 28 sq. units.

922 Views

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

2842 Views