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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).

763 Views

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.

228 Views

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

1273 Views

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

542 Views

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.

337 Views

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).

It is given that: point P(x, y) is equidistant from the points A(2, 5) and B(-3, 7)

rightwards double arrow space PA space equals space PB rightwards double arrow square root of left parenthesis 2 minus straight x right parenthesis squared plus left parenthesis 5 minus straight y right parenthesis squared end root equals square root of left parenthesis negative 3 minus straight x right parenthesis squared plus left parenthesis 7 minus straight y right parenthesis squared end root rightwards double arrow square root of left parenthesis 2 right parenthesis squared plus left parenthesis straight x right parenthesis squared minus 2 left parenthesis 2 right parenthesis left parenthesis straight x right parenthesis plus left parenthesis 5 right parenthesis squared plus left parenthesis straight y right parenthesis squared minus 2 left parenthesis 5 right parenthesis left parenthesis straight y right parenthesis end root equals square root of left parenthesis negative 3 right parenthesis squared plus left parenthesis straight x right parenthesis squared minus 2 left parenthesis negative 3 right parenthesis left parenthesis straight x right parenthesis plus left parenthesis 7 right parenthesis squared plus left parenthesis straight y right parenthesis squared minus 2 left parenthesis 7 right parenthesis left parenthesis straight y right parenthesis end root rightwards double arrow square root of 4 plus straight x squared minus 4 straight x plus 25 plus straight y squared minus 10 straight y end root equals square root of 9 plus straight x squared plus 6 straight x plus 49 plus straight y squared minus 14 straight y end root rightwards double arrow square root of straight x squared plus straight y squared minus 4 straight x minus 10 straight y plus 29 end root equals square root of straight x squared plus straight y squared plus 6 straight x minus 14 straight y plus 58 end root

Squaring both sides,
x² + y² - 4x - 10y + 29
= x² + y² + 6x - 14y + 58
⇒ -4x - 6x - 10y + 14y + 29 - 58 = 0
⇒    -10x + 4y - 29 = 0
⇒    -(10x - 4y + 29) = 0
⇒    10x — 4y + 29 = 0
⇒    10x -4y + 29 = 0. Ans.

283 Views

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

154 Views

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.

978 Views

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.

454 Views