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Home » If (– 4, 3) and (4, 3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the interior of the triangle.
If (– 4, 3) and (4, 3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the interior of the triangle.
CBSE | Class 10 | Coordinate Geometry | Exercise 7.4 | Maths | NCERT Exemplar
If (– 4, 3) and (4, 3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the interior of the triangle.

Solution:

NCERT Exemplar Class 10 Maths Chapter 7 Ex. 7.4 Question 1

Let (x,y) be the vertices.

The distance between (x,y) & (4,3) is =\text{ }\surd ({{\left( x-4 \right)}^{2}}~+\text{ }{{\left( y-3 \right)}^{2}})……(1)

The distance between (x,y) & (-4,3) is =\surd ({{\left( x+4 \right)}^{2}}~+\text{ }{{\left( y-3 \right)}^{2}})……(2)

The distance between (4,3) &(-4,3) is =\surd ({{\left( 4+4 \right)}^{2}}~+\text{ }{{\left( 3-3 \right)}^{2}})\text{ }=\text{ }\surd \left( 8 \right){}^\text{2}=8

Now according to the given question,

Eq. (1) = Eq.(2)

\left( x-4 \right){}^\text{2}=\left( x+4 \right){}^\text{2}

x{}^\text{2}-8x+16=x{}^\text{2}+8x+16

16x=0

x=0

Now, equation (1) = 8

\left( x-4 \right){}^\text{2}+\left( y-3 \right){}^\text{2}=64……… (3)

On substituting the value of x in eq.(3)

\left( 0-4 \right){}^\text{2}+\left( y-3 \right){}^\text{2}=64

\left( y-3 \right){}^\text{2}=64-16

\left( y-3 \right){}^\text{2}=48

y-3=\left( + \right)4\surd 3

y=3\left( + \right)\text{ }4\surd 3

Neglect y\text{ }=\text{ }3+4\surd 3as if y\text{ }=\text{ }3+4\surd 3 then origin cannot interior of triangle

As a result, the third vertex =\text{ }\left( 0,\text{ }3-4\surd 3 \right)

i

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