Question

prove that the points P(0,-1),Q(-2,3),R(6,7),S(8,3)are the vertices of a rectangle PQRS

Answer 1

Answer:

Find the distances between PQ, QR, RS, PS, PR and QS. Then see whether its opposite sides are equal, then it is a rectangle.

Answer 2

Answer:

yes , it is a rectangle

Step-by-step explanation:

We know opposite side of rectangle is equal.

so, will find the length of quadrilateral ABCD

PQ = √(0-(-2) )^2 + (-1-3)^2 = √4 + 16 = √20unit

QR = √(-2-6)^2 + (3-7)^2 = √64+16 = √80 = 4√5unit

RS = √(6-8)^2 + (7-3)^2 = √ 4+16 = √20

SP = √(8-0)^2 + (3-(-1))^2 = √64+16 = √80 = 4√5

now we find the length of diagonal

PR = √(0-6)^2 + (-1-7)^2 = √36+64 = √100 = 10unit

QS = √(-2-8)^2 + (3-3)^2 = √100 = 10unit

from the above we find that opposite side of quadrilateral ABCD and diagonals are equal.

si, it is a rectangle