If (-5,3) and (5,3) are two vertices of an equilateral triangle, then find coordinates of the third vertex, given that…

CBSE Class 10 Maths PYQ · Coordinate Geometry · Application · 3 Marks · March 2023 · Standard

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1173 Marks · March 2023 · Standard

If $(-5,3)$ and $(5,3)$ are two vertices of an equilateral triangle, then find coordinates of the third vertex, given that origin lies inside the triangle. (Take $\sqrt{3}= 1.7$)

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Let the third vertex be $(x,y)$
$A (-5,3)$ $B(5,3)$ $C(x,y)$
$AB=10=AC$
$AC^2=100$
$(-5-x)^2+(3-y)^2 = (5-x)^2+(3-y)^2$
$20x =0$
$x=0$
$(3-y)^2=75$
$3-y = \pm 5\sqrt{3}$
$y=3-5\sqrt{3}$
$y= -5.5$
The coordinates of the third vertex are $(0,-5.5)$