Solve

Guides

Question

Open in App

Solution

Verified by Toppr

The given points are P(2,-1), Q(3,4), R(-2,3) and S(-3,-2).We have

PQ=√(3−2)2+(4+1)2=√12+52=√26units

QR=√(−2−3)2+(3−4)2=√25+1=√26units

RS=√(−3+2)2+(−2−3)2=√1+25=√26units

SP=√(−3−2)2+(−2−3)2=√26units

PR=√(−2−2)2+(3+1)2=√16+16=4√2units

and, QS=√(−3−3)2+(−2−4)2=√36+36=6√2units

∴PQ=QR=RS=SP=√26units

and, PR≠QS

This means that PQRS is quadrilateral whose sides are equal but diagonals are not equal.

Thus, PQRS is a rhombus but not a square.

.Now, Area of rhombus PQRS=12×(Productoflengthsofdiagonals)

⇒AreaofrhombusPQRS=12×(PR×QS)

⇒AreaofrhombusPQRS=(12×4√2×6√2)sq.units=24sq.units

Was this answer helpful?

14