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Home » Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.
Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.
CBSE | Class 10 | Coordinate Geometry | Maths | NCERT
Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.

Solution:

Any isosceles triangle has two sides that are equal. We’ll find the distance between all of the points to see if they’re vertices of an isosceles triangle.

Let the vertices A, B, and C be represented by the points (5, – 2), (6, 4), and (7, – 2), respectively.

AB=\sqrt{{{\left( 6-5 \right)}^{2}}+{{\left( 4+2 \right)}^{2}}}=\sqrt{{{\left( -1 \right)}^{2}}+{{\left( 6 \right)}^{2}}}=\sqrt{37}

BC=\sqrt{{{\left( 7-6 \right)}^{2}}+{{\left( -2-4 \right)}^{2}}}=\sqrt{{{\left( -1 \right)}^{2}}+{{\left( 6 \right)}^{2}}}=\sqrt{37}

CA=\sqrt{{{\left( 7-5 \right)}^{2}}+{{\left( -2+2 \right)}^{2}}}=\sqrt{{{\left( -2 \right)}^{2}}+{{\left( 0 \right)}^{2}}}=2

As a result, AB=BC=\sqrt{37}

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