Given coordinates of a quadilaretal RSTU, in order to know each pair sides if any that are parallel and which are perpendicular to the coordinates of the vertices, we will find the equation of each line of the quadilateral using those coordinates as shown;
For line RS wth coordinates R(0,0) S (6,3).
The equation of aline is y = mx+c
m is the slope and c is the intercept.
slope of the line RS = 3-0/6-0
slope of RS = 3/6 = 1/2
for the intercept, substitute any of the point and the slope into the equation y = mx+c
using (6,3)
3 = 1/2(6) + c
3 = 3+c
c = 3-3
c = 0
equatio of line RS is y = 1/2 x
For line RT wth coordinates R(0,0) T (5,5).
The equation of aline is y = mx+c
m is the slope and c is the intercept.
slope of the line RT = 5-0/5-0
slope of RT = 5/5 = 1
for the intercept, substitute any of the point and the slope into the equation y = mx+c
using (0,0)
0 = 0 + c
c = 0
equatio of line RT is y = 1x or y =x
or
For line RU wth coordinates R(0,0) U (-1,2).
The equation of aline is y = mx+c
m is the slope and c is the intercept.
slope of the line RT = 2-0/-1-0
slope of RU = -2
For line ST wth coordinatesS(6,3) T (5,5).
The equation of a line is y = mx+c
m is the slope and c is the intercept.
slope of the line ST = 5-3/5-6
slope of ST = 2/-1
slope of line ST = -2
For line SU wth coordinatesS(6,3) U (-1,2).
slope of the line SU = 2-3/-1-6
slope of SU = -1/-7
slope of line SU = 1/7
For line TU wth coordinates T(5,5) U (-1,2).
slope of the line TU = 2-5/-1-5
slope of TU = -3/-6
slope of line TU = 1/2
Note that for two lines to be parallel they must have the same slope
From the gotten value, the line with the same slope are TU and RS, RU and ST
For two lines to be perpendicaular, the product of their slope must be -1
The lines with the product of the slope -1 are ST and TU, RU and TU (note that the product of this slope gives -1, hence they are perpendicular)
Pair 1 = Parallel (same slope)
Pair 2 = perpendicular (product of both slopes is -1)
Pair 3 = perpendicular (product of both slopes is -1)
Pair 4 = perpendicular (product of both slopes is -1)
Pair 5= Parallel (same slope)
Pair 6 = perpendicular (product of both slopes is -1)
Look at the explanation well to be able to understand better