# Thread: [SOLVED] rhombus analytic geometry

1. ## [SOLVED] rhombus analytic geometry

just tell me how to solve the first step. i have no idea how to start

2. Originally Posted by helloying
just tell me how to solve the first step. i have no idea how to start
Show that $(-1, 2)$ lies on the line $y=x+3$ and show that it's equidistant from P and R.

3. Originally Posted by helloying
just tell me how to solve the first step. i have no idea how to start
If PQRS is a rhombus, then its 4 sides are equal in lengths.
So, PS = RS
Let (a,b) be the coordinates of S.
Then,
((a+3)^2 +(b -8)^2 = (a -5)^2 +(b -4))^2 -----(1)

In the line y = x+3,
b = a +3 -----------(2)

Solve those two equations simultaneously to find "a" and b.

---------------------
For the coordinates of Q:

See the relation of point P to point S.
It must be the same retion of point Q to point R.
Thus, Q is (5 +(-3 -a)),(4 +(8 -b))

4. Is that an AS level paper?

Anyway, the figure is a rhombus, so all its sides are equal. All you have to do is... FIRST, use the distance formula to show that $(-1, 2)$ is equidistant from $P (-3, 8)$ and $R (5, 4)$, or show that $SR = PR$. SECONDLY, plug in $(-1, 2)$ into $y = x + 3$ and show that it satisfies the equation.

I hope that helps.

me07.

5. [quote=ILoveMaths07;193459]Is that an AS level paper?

Nope!this is not AS level. This is O level