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Coordinate Geometry

Short Answer Type

191. Name the type of triangle formed, if any, by the following points and give reason for your answer :

left parenthesis straight a comma space straight a right parenthesis comma space left parenthesis negative straight a comma space minus straight a right parenthesis comma space left parenthesis negative straight a square root of 3 comma space straight a square root of 3 right parenthesis

80 Views

Long Answer Type

192. Name the type of triangle formed, if any, by the following points and give reason for your answer:

left parenthesis 1 comma space minus 1 right parenthesis comma space space open parentheses fraction numerator negative 1 over denominator 2 end fraction comma space 1 half close parentheses space left parenthesis 1 comma space 2 right parenthesis

92 Views

Short Answer Type

193. Name the type of triangle formed, if any, by the following points and give reason for your answer:

open parentheses negative 2 comma space 0 close parentheses comma space open parentheses negative 4 comma space minus 2 square root of 3 close parentheses comma space left parenthesis negative 6 comma space straight C right parenthesis.

98 Views

194. Determine by distance formula, whether the given points are collinear :
(1, 2), (9, 3) and (17, 4)

162 Views

195. Determine by distance formula, whether the given points are collinear :
(-1, 2), (5, 0) and (2, 1).

124 Views

196. Find a point on jr-axis which is equidistant from (-5, -2) and (3, 2).

Let the required point be ‘P’ which is on the y-axis, so, its abscissa = 0 and ordinate (say) = y.
Thus co-ordinates of the point P are (0, y).
Let the given points be A(-5, -2) and B(3, 2).
It is given that: AP = BP

rightwards double arrow space square root of left parenthesis 0 minus left parenthesis negative 5 right parenthesis right parenthesis squared plus left parenthesis straight y minus left parenthesis negative 2 right parenthesis right parenthesis squared end root equals square root of left parenthesis 0 minus 3 right parenthesis squared plus left parenthesis straight y minus 2 right parenthesis squared end root rightwards double arrow space space square root of left parenthesis 0 plus 5 right parenthesis squared plus left parenthesis straight y plus 2 right parenthesis squared end root equals square root of left parenthesis negative 3 right parenthesis squared plus left parenthesis straight y minus 2 right parenthesis squared end root rightwards double arrow space equals space square root of 25 plus straight y squared plus 4 plus 4 straight y end root equals square root of 9 plus straight y squared plus 4 minus 4 straight y end root rightwards double arrow square root of straight y squared plus 4 straight y plus 29 end root equals square root of straight y squared minus 4 straight y plus 13 end root

Squaring both side, we get
y² + 4y + 29 = y² - 4y + 13
⇒    4y + 4y = 13 - 29
⇒    8y = -16
⇒    y = -2
Therefore, the required point is (0, -2).

85 Views

197. Find the point on x-axis which is equidistant from the points (2, -5) and (-2,

148 Views

198. Find the relation between x and y such that point (x, y) is equidistant from the points (6, -1) and (2, 3).

122 Views

199. Show that the points A(2, -2), B(14, 10), C(11, 13) and D(-1, 1) are the vertices of a rectangle.

485 Views

Long Answer Type

200. Show that the points A(5, 6), B(1, 5), C(2, 1) and D(6, 2) arc the vertices of a square.

162 Views