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Coordinate Geometry

Long Answer Type

201. Show that (1, -1) is the centre of the circle circumscribing the triangle whose angular points are (4, 3), (-2, 3) and (6, -1).

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Short Answer Type

202. If A(2, -1), B(3, 4), C(-2, 3) and D(-3, -2) be four points in a plane, show that ABCD is a rhombus but not a square.

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203. Show that the points (7, 10), (-2, 5) and (3, -4) are the vertices of an isosceles right triangle.

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204. Show that A(-3, 2), B(-5, -5), C (2,-3) and D(4, 4) arc the vertices of a rhombus.

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205. Observe the graph given below and state whether triangle ABC is scalene, isosceles or equilateral. Justify your answer. Also find its area.

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206. Find the values of x for which the distance between the point P(2, -3) and Q(x, 5) is 10 units.

Given points be P(2, -3) and Q(x, 5).
It is also given that PQ = 10 units
Here, we have x₁ = 2, y₁ = -3, x₂ = x, y₂ = 5

$Now comma space space PQ space equals space square root of left parenthesis straight x subscript 2 minus straight x subscript 1 right parenthesis squared plus left parenthesis straight y subscript 2 minus straight y subscript 1 right parenthesis squared end root rightwards double arrow space space space space space space 10 space equals space square root of left parenthesis straight x minus 2 right parenthesis squared plus left parenthesis 5 plus 3 right parenthesis squared end root$
Squaring both sides, we get

Given points be P(2, -3) and Q(x, 5).It is also given that PQ = 10 un

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207. Find a relation between x and y such thai the point P(x, y) is equidistant from the points A(2, 5) and B(-3, 7).

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208. If the distances of P (x, y) from the points A(3, 6) and B(-3, 4) are equal prove that 3x + y = 5

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209. If the points A (4, 3) and B (x, 5) are on the circle with the centre O (2,3), find the value of x.

Fig. 7.28.

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Long Answer Type

210. The line joining the points (1, -2) and (-3, 4) is trisected. Find the co-ordinates of the points of trisection.

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