Search any question & find its solution
Question:
Answered & Verified by Expert
The points $(2,-2),(8,4),(4,6)$ and $(-1,1)$ in order are the vertices of which one of the following quadrilaterals?
Options:
Solution:
2582 Upvotes
Verified Answer
The correct answer is:
Trapezium
Let points be $\mathrm{A}(2,-2), \mathrm{B}(8,4), \mathrm{C}(4,6)$ and $\mathrm{D}(-1,1)$ in
order and are vertices of a quadrilateral. $\mathrm{AB}^{2}=(8-2)^{2}+(4+2)^{2}=36+36=72$
$\mathrm{BC}^{2}=(4-8)^{2}+(6-4)^{2}=16+4=20$
$\mathrm{CD}^{2}=(4+1)^{2}+(6-1)^{2}=25+25=50$
$\mathrm{AD}^{2}=(2+1)^{2}+(-2-1)^{2}=9+9=18$
Thus $\mathrm{AB} \neq \mathrm{BC} \neq \mathrm{CD} \neq \mathrm{AD}$
Hence, quadrilateral is a trapezium.
order and are vertices of a quadrilateral. $\mathrm{AB}^{2}=(8-2)^{2}+(4+2)^{2}=36+36=72$
$\mathrm{BC}^{2}=(4-8)^{2}+(6-4)^{2}=16+4=20$
$\mathrm{CD}^{2}=(4+1)^{2}+(6-1)^{2}=25+25=50$
$\mathrm{AD}^{2}=(2+1)^{2}+(-2-1)^{2}=9+9=18$
Thus $\mathrm{AB} \neq \mathrm{BC} \neq \mathrm{CD} \neq \mathrm{AD}$
Hence, quadrilateral is a trapezium.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.