# How to calculate the coordinate of a point which depends on other points on a plane with specific distances

I have $8$ points on a plane $(x_1,y_1)....(x_8,y_8)$ among these $8$ points I know the coordinates for $7$ points and I have to find the $8^{th}$ point.

Each points has the difference between all other points. I am also having other info like Euclid dist and angle between the points. How can I identify the coordinate position of the $8^{th}$ point?

The information is:
1) I have pairwise difference between each point as diff[diff $x_1$,diff $y_1$]=$(x_1,y_1)-(x_2,y_2)$.
2) Pair wise distance between the points: $d= \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$
3) Pair wise angle/direction of the points $=a\tan{2}((p_1\cdot y-p_2 \cdot y),(p_1\cdot x-p_2\cdot x))\cdot \frac{180}{3.14}$ the identified point should be best fit for all other points.

• I would also recommend finding a better way to signify your 'diff'. Perhaps $\Delta$? I'm not positive what would be an appropriate substitute. – Vincent Jul 30 '14 at 5:50
• So you have $d_1^2= (x_1-x)^2+(y_1-y)^2,\dots, d_7^2=(x_7-x)^2+(y_7-y)^2$ and you want to know $(x,y)$. Isn't it straightforward? (Just eliminate $x^2$ and $y^2$ using any $3$ equations and you have a linear system of $2$ equations in two unknown $x,y$.) – Quang Hoang Jul 30 '14 at 6:37