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

The points \[A(9,0),\] \[B(9,6),\] \[C(-9,6)\] and \[D(-9,0)\] are the vertices of a:

A) square

B) rectangle

C) rhombus

D) trapezium

Correct Answer: B

Solution :

[b] \[AB=\sqrt{{{(9-9)}^{2}}+{{(6-0)}^{2}}}=\sqrt{{{0}^{2}}+{{6}^{2}}}=6\]

\[BC=\sqrt{{{(-9-9)}^{2}}+{{(6-6)}^{2}}}=\sqrt{{{(-18)}^{2}}+{{0}^{2}}}=18\]

\[CD=\sqrt{{{(-9+9)}^{2}}+{{(0-6)}^{2}}}=\sqrt{{{0}^{2}}+{{(-6)}^{2}}}=6\]

\[DA=\sqrt{{{(9+9)}^{2}}+{{(0-0)}^{2}}}=\sqrt{{{(18)}^{2}}}=18\]

\[\therefore \,\,\,\,\,\,\,AB=CD\] and \[BC=DA\]

Now, \[AC=\sqrt{{{(-9-9)}^{2}}+{{(6-0)}^{2}}}=\sqrt{{{(18)}^{2}}+{{6}^{2}}}=\sqrt{360}\]and \[A{{C}^{2}}=A{{B}^{2}}+B{{C}^{2}}\]

\[\therefore \] Angle B is a right angle.

Hence, ABCD is a rectangle.