Q. 44.2( 172 Votes )

# Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle

Answer :

Distance between two points A(x_{1}, y_{1}) and B(x_{2}, y_{2}) is given by

D = √(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}

Let us assume that points (5, - 2), (6, 4), and (7, - 2) are representing the vertices A, B, and C of the given triangle respectively as shown in the figure.

AB = [(5- 6)^{2} + (-2- 4)^{2}]^{1/2}

=

=

BC = [(6- 7)^{2} + (4 + 2)^{2}]^{1/2}

=

=

CA = [(5- 7)^{2} + (-2+ 2)^{2}]^{1/2}

=

= 2

Therefore, AB = BC

As two sides are equal in length, therefore, ABC is an isosceles triangle

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