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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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Let the given points be A (a, a), B(-a, -a) and ThenSince, AB = BC

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

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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

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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).

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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,

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

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

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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.

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