Question

Show that the points P(2;-2) Q(8;4) R(5;7) S(-1;1) taken in order forms a rectangle

Answer 1

the vertex are showing a rectangle

Answer 2

opposite sides of rectangle are congruent
d (P, Q)=
$\sqrt{(8 - 2) {}^{2} } + \sqrt{(4 + 2} ) {?}^{2}$

=
$\sqrt{36 + 36}$


=
$\sqrt{72}$

=
$\sqrt{8 \times 9}$


=
$3 \sqrt{8}$
similarly, d (Q, R), d (R, S)and d (P, S) will be
$3 \sqrt{8}$
Hence points P, Q, R and S form a rectangle