Question

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

Answer 1

M (RS) = 1/2
m (ST) = -2
m (TU) = 1/2
m (RU) = -2

RS -- is b) parallel to -- TU (same slopes)

RS -- is c) perpendicular to -- ST (negative reciprocal slopes)
RS -- is c) perpendicular to -- RU (negative reciprocal slopes)
TU -- is c) perpendicular to -- ST (negative reciprocal slopes)
TU -- is c) perpendicular to -- RU (negative reciprocal slopes)

ST -- is b) parallel to -- RU (same slopes)

Since 4 perpendicular lines (right angles) and 2 sets of parallel lines, and two sets of equal lengths, RSTU is a rectangle.

Answer 2

Answer:

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:

$\sqrt{(c-a)^2+(d-b)^2}$

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° )