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

The area of the triangle PQR is:

A) 21 sq. units

B) 35 sq. units

C) 42 sq, units

D) 45 sq, units

Correct Answer: A

Solution :

The coordinates of the vertices P, Q and \[R(6,9)\], \[(2,3)\]and \[(9,3)\] respectively.

Now, base of the

\[\Delta PQR=QR=\sqrt{{{(9-2)}^{2}}+{{(3-3)}^{2}}}\]

\[=\sqrt{49+0}=7\] units

and height of the \[\Delta PQR\]=Perpendicular distance from the vertex P to the base \[QR=(9-3)=6\] units.

\[\therefore \] Area of

\[\Delta PQR=\frac{1}{2}\times \text{base}\times \text{height =}\frac{1}{2}\times 7\times 6=21\,sq.\]. units

So, option [a] is Correct.