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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:

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

Let the given points be

straight A left parenthesis 1 comma space minus 1 right parenthesis comma space space straight B open parentheses negative 1 half comma space 1 half close parentheses space space and space straight C left parenthesis 1 comma space 2 right parenthesis space then

AB space equals space square root of open parentheses negative 1 half close parentheses squared plus open parentheses 1 half minus left parenthesis negative 1 right parenthesis close parentheses end root rightwards double arrow space AB space equals space square root of open parentheses fraction numerator negative 1 minus 2 over denominator 2 end fraction close parentheses squared plus open parentheses fraction numerator 1 over denominator 2 plus 1 end fraction 1 close parentheses squared end root rightwards double arrow space AB space equals space square root of open parentheses fraction numerator negative 3 over denominator 2 end fraction close parentheses squared plus open parentheses 3 over 2 close parentheses squared end root rightwards double arrow space AB space equals space square root of 9 over 4 plus 9 over 4 end root

BC space equals space square root of open curly brackets 1 minus open parentheses fraction numerator negative 1 over denominator 2 end fraction close parentheses close curly brackets squared plus open parentheses 2 minus 1 half close parentheses squared end root rightwards double arrow space BC space equals space square root of open parentheses 1 plus 1 half close parentheses squared plus open parentheses 2 minus 1 half close parentheses squared end root rightwards double arrow space BC space equals space square root of open parentheses 1 plus 1 half close parentheses squared plus open parentheses 2 minus 1 half close parentheses squared end root rightwards double arrow space BC space equals space square root of open parentheses fraction numerator 2 plus 1 over denominator 2 end fraction close parentheses squared plus open parentheses fraction numerator 4 minus 1 over denominator 2 end fraction close parentheses squared end root rightwards double arrow space BC space equals space square root of open parentheses 3 over 2 close parentheses squared plus open parentheses 3 over 2 close parentheses squared end root rightwards double arrow space BC space equals space square root of 9 over 4 plus 9 over 4 end root rightwards double arrow space BC space equals space 3 over 2 square root of 2 and space space AC space equals space square root of left parenthesis 1 minus 1 right parenthesis squared plus left curly bracket 2 minus left parenthesis negative 1 right parenthesis right curly bracket squared end root rightwards double arrow space AC space equals space square root of 0 plus left parenthesis 2 plus 1 right parenthesis squared end root rightwards double arrow space AC space equals space square root of 0 plus left parenthesis 3 right parenthesis squared end root rightwards double arrow space AC space equals space square root of 9 space equals space 3

Since, AB = BC
So, the given points form an isosceles triangle.

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).

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