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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).

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

Let the given points be A(K. 3), B(6. -2) and C(-3, 4).
Here, we have x₁ = K,    fy₁ = 3
x₂ = 6,    y₂ = -2
and    x₃ = -3, y₃ = 4
Given three points, arc collinear if.

$straight x subscript 1 left parenthesis straight y subscript 2 minus straight y subscript 3 right parenthesis plus straight x subscript 2 left parenthesis straight y subscript 3 minus straight y subscript 1 right parenthesis plus straight x subscript 3 left parenthesis straight y subscript 1 minus straight y subscript 2 right parenthesis equals 0 rightwards double arrow space straight K left parenthesis negative 2 minus 4 right parenthesis plus 6 left parenthesis 4 minus 3 right parenthesis plus left parenthesis 3 right parenthesis left parenthesis 3 plus 2 right parenthesis equals 0 rightwards double arrow space space straight K left parenthesis negative 6 right parenthesis plus 6 left parenthesis 1 right parenthesis plus left parenthesis negative 3 right parenthesis space straight x space 5 space equals space 0 rightwards double arrow space space minus 6 straight K plus 6 minus 15 equals 0 rightwards double arrow negative 6 straight K minus 9 equals 0 rightwards double arrow space space minus 6 straight K space equals space 9 rightwards double arrow straight K equals fraction numerator 9 over denominator negative 6 end fraction equals fraction numerator negative 3 over denominator 2 end fraction$

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