# Thread: Parallelogram (point coordinates, diagonal, angle, straight line)

1. ## Parallelogram (point coordinates, diagonal, angle, straight line)

Hey guys! I will not be too long in pre-explanations - my cousin has big problem with math, however, i could not help him with this one. Hope you will.

Task. Given parallelogram's PRST three points R, S, T:

a) Calculate coordinates of a point P and construct parallelogram;
b) Write an equation of diagonal PS;
c) Calculate angle between diagonal PS and ST;
d) Write an equation for a line, which goes through centre of parallelogram and perpendicular to PS.

If you guys could also tell me what theory you used, that would be very much appreciated because i want to learn, not just get an answer. BIG BIG thanks!

2. ## Re: Parallelogram (point coordinates, diagonal, angle, straight line)

Originally Posted by Ernest1990
Task. Given parallelogram's PRST three points R, S, T:
a) Calculate coordinates of a point P and construct parallelogram;
b) Write an equation of diagonal PS;
c) Calculate angle between diagonal PS and ST;
d) Write an equation for a line, which goes through centre of parallelogram and perpendicular to PS.
1) Find the slope of the lines $s_{RS}:\overleftrightarrow {RS}\;\& \,s_{TS}:\overleftrightarrow {TS}$.

2) Write the equation of the line $\overleftrightarrow {PT}$ with slope $s_{RS}$
Write the equation of the line $\overleftrightarrow {PR}$ with slope $s_{TS}$

3) Find $\;\left\{ P \right\} = \,\overleftrightarrow {PT}\cap\,\overleftrightarrow {PR}\,$

Now you know the coordinates of a point P.
The rest follows.