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

The fourth vertex of a rectangle whose three vertices taken in order are \[(4,1),\] \[(7,4),\] \[(13,-2)\]is:

A) \[(10,5)\]

B) \[(10,-5)\]

C) \[(8,3)\]

D) \[(8,-3)\]

Correct Answer: B

Solution :

[b] Daygram

Mid-points of diagonal of a rectangle coincide

\[\therefore \,\,\,\,\,\,\left( \frac{13+4}{2},\frac{1-2}{2} \right)=\left( \frac{x+7}{2},\frac{y+4}{2} \right)\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=10\] and \[y=-5\]

Hence, fourth vertex is \[D(10-5)\]