Q. 184.3( 10 Votes )

An equilateral triangle has two vertices at the points (3, 4) and ( - 2, 3), find the coordinates of the third vertex.

Answer :

Given: The points (3, 4) and ( - 2, 3).


To find: The coordinate of the third vertex.


Formula Used:


The distance between the points (x1,y1) and (x2,y2) is:


Distance


Explanation:



Let the Vertices of a triangle ABC are: A (3, 4) and B ( - 2, 3), and C(x, y)


Length of side AB


Length of side AB units


Length of side BC units


Length of side AC units


As triangle is equilateral, (AB)2 = (BC)2





…….. (1)


(AB)2 = (AC)2





….. (2)


On subtracting eqn (2) from (1), we get






…… (3)


(AC)2= (BC)2




……. (4)


Solving equations (3) and (4), we get



Therefore, coordinates of C are


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