Given quadrilateral rstu, determine if each pair of sides (if any) are parallel and which are perpendicular for the coordinates of the vertices.

r(0, 0), s(6, 3), t(5, 5), u(-l, 2)

the pairs of sides are shown in the pictures below,, your options for the answer to each of them are
a) none
b) parallel
c) perpendicular

We are given a quadrilateral RSTU such that the coordinates of the vertices are given as:

R(0, 0), S(6, 3), T(5, 5), U(-l, 2)

the length of the line segment could be calculated with the help of distance formula:

since the length of line segment A(a,b) and B(c,d) is calculated as:

on graphing the quadrilateral we observe that it is a rectangle such that:

length of segment RS=TU=3√5 units.

and length of segment UR=ST=√5 units.

Also side RS || TU

and ST || UR.

From the figure we could observe that:

Pair 2:

RS is perpendicular to ST.

Pair 3:

RS is perpendicular to RU.

Pair 4:

TU is  perpendicular to ST.

Pair 6:

TU is  perpendicular to RU.

( Since in rectangle each of the interior angle are equal and equal to 90° )