10th Class Mathematics Coordinate Geometry Question Bank Case Based (MCQs) - Coordinate Geometry

The type of triangle ABC is:

A) equilateral triangle

B) isosceles triangle

C) scalene triangle

D) right triangle

Correct Answer: B

Solution :

The coordinates of the vertices A, B and C are \[\left( \frac{9}{2},9 \right),\]\[(3,7)\]and \[(6,7)\]respectively.

Now, \[AB=\sqrt{{{\left( 3-\frac{9}{2} \right)}^{2}}+{{(7-9)}^{2}}}=\sqrt{\frac{9}{4}+4}=\frac{5}{2}=2.5\] units

\[BC=\sqrt{{{(6-3)}^{2}}+{{(7-7)}^{2}}}=3\]units

and \[AC=\sqrt{{{\left( \frac{9}{2}-6 \right)}^{2}}+{{(9-7)}^{2}}}=\sqrt{\frac{9}{4}+4}=\frac{5}{2}=25\] units

As, two sides AB and AC are equal, it is an isosceles triangle.

Moreover, \[B{{C}^{2}}\ne A{{B}^{2}}+A{{C}^{2}}\]

\[\therefore \] ABC is not a right triangle.

So, option [b] is correct,