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

Four points \[(0,-1),\] \[(6,7),\] \[(-2,3)\] and \[(8,3)\] are the vertices of a rectangle. Then its area is:

A) \[50\,sq.\,units\]

B) \[45\,sq.\,units\]

C) \[40\,sq.\,units\]

D) \[30\,sq.\,units\]

Correct Answer: C

Solution :

[c] Let \[A(0,-1),\]\[B(6,7),\]\[C(-2,3)\] and \[D(8,3)\] be the given vertices of a rectangle. Then,

\[AD=\sqrt{{{(8-0)}^{2}}+{{(3+1)}^{2}}}=\sqrt{64+16}=4\sqrt{5}\]

and \[AC=\sqrt{{{(-2-0)}^{2}}+{{(3+1)}^{2}}}=\sqrt{4+16}=2\sqrt{5}\]

\[\therefore \] Area of rectangle \[ADBC=AD\times AC\]

\[=4\sqrt{5}\times 2\sqrt{5}=40\,\,sq.\] units.