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

• Oct 18th 2011, 11:22 AM
Ernest1990
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!
• Oct 18th 2011, 11:45 AM
Plato
Re: Parallelogram (point coordinates, diagonal, angle, straight line)
Quote:

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 $\displaystyle s_{RS}:\overleftrightarrow {RS}\;\& \,s_{TS}:\overleftrightarrow {TS}$.

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

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

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