10th Class Mathematics Coordinate Geometry Question Bank MCQs - Coordinate Geometry

The points \[(-4,0),\] \[(4,0),\] \[(0,3)\] are the vertices of a/an: (NCERT EXEMPLAR)

A) right triangle

B) isosceles triangle

C) equilateral triangle

D) scalene triangle

Correct Answer: B

Solution :

[b] Let \[A(-4,0),\] \[B(4,0),\] \[C(0,3)\]are the given vertices.

Now, distance between \[A(-4,0)\] and \[B(4,0)\]

\[AB=\sqrt{{{[4-(-4)]}^{2}}+{{(0-0)}^{2}}}=\sqrt{{{(4+4)}^{2}}}=\sqrt{{{8}^{2}}}=8\]Distance between \[B(4,0)\] and \[C(0,3)\]

\[BC=\sqrt{{{(0-4)}^{2}}+{{(3-0)}^{2}}}=\sqrt{16+9}=\sqrt{25}=5\]

Distance between \[A(-4,0)\] and \[C(0,3)\].

\[AC=\sqrt{[0-{{(-4)}^{2}}]+{{(3-0)}^{2}}}=\sqrt{16+9}=\sqrt{25}=5\] \[BC=AC\]

Hence, \[\Delta ABC\] is an isosceles triangle because an isosceles triangle has two sides equal.