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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

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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.

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

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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).

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

We know that any point on x-axis is of the form P (x, 0).
Since, P (x, 0) is equidistant from A (2, -5) and B (-2, 9)

$therefore space space PA space equals space PB space equals space rightwards double arrow space PA squared equals PB squared rightwards double arrow space left parenthesis straight x minus 2 right parenthesis squared plus left parenthesis 0 plus 5 right parenthesis squared equals left parenthesis straight x plus 2 right parenthesis squared plus left parenthesis 0 minus 9 right parenthesis squared rightwards double arrow straight x squared minus 4 straight x plus 4 plus 25 equals straight x squared plus 4 straight x plus 4 plus 81 rightwards double arrow negative 4 straight x minus 4 straight x space equals space 81 minus 25 rightwards double arrow space minus 8 straight x space equals space 56 rightwards double arrow space straight x space equals space fraction numerator 56 over denominator negative 8 end fraction equals negative 7$
Hence, the required point is (-7, 0).