Q. 264.7( 3 Votes )

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Answer :

Given: Vertices (2, 0) and (2, 5).


To find: The third vertex


Formula Used:


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


Distance


Explanation:


Vertices of an isosceles are A (2, 0) and B (2, 5).


Let the third vertex is P (x, y)


Using distance formula


Length of side PA units


Length of side PB units


Since PA = PB



On squaring both sides, we get


(x - 2)2 + y2 = (x - 2)2 + (y - 5)2


x2 - 4x + 4 + y2 = x2 - 4x + 4 + y2 - 10y + 25


,


Also, PA = 3



On squaring both sides, we get


(x - 2)2 + (y)2 = 9


x2 - 4x + 4 + y2= 9


x2 - 4x + y2 = 5


On substituting ,





Using the quadratic formula:





Therefore, the coordinates of the third vertex are: ;


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