Question

if p ( 2,-1) q ( 3,4 ) r ( -2,3) and s ( -3,-2) are in same plane then show that pqrs is a rhombus not a square

Answer 1

Answer:

Step-by-step explanation:

P ( 2,-1) , Q ( 3,4 ) , R ( -2,3) , S ( -3,-2)

PQ = √(1² + 5²) = √26

QR = √(5² + 1²) = √26

RS = √(1² + 5²) = √26

PS = √(5² + 1²) = √26

All the sides are equal. So PQRS can either be square or rhombus.

Now, tell is check the diagonal PR.

PR = √(4² + 4²) = √32

If PQRS is square, then PQ² + QR² = PR²

PQ² + QR² = 26 + 26 = 52 ≠ 32

So PQRS is not square. Hence it rhombus.