Co-ordinate Geometry — Chapter Summary

Count the separation between two points

Count the separation between two points by subtracting their coordinates. For points P, Q, and R with coordinates -1, -5, and 4, the distances are 4 a

For two points A(x1

For two points A(x1,y1) and B(x2,y2), the distance is AB = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}. The formula comes from a right triangle formed by horizon

For a point P(x

For a point P(x,y), the distance from the origin O(0,0) is d(O,P) = \sqrt{x^2 + y^2}. This is just the distance formula with one point at the origin.

If P(x

If P(x,y) divides the segment joining A(x1,y1) and B(x2,y2) in the ratio m:n, then the coordinates of P are \left((mx2 + nx1)/(m + n),(my2 + ny1)/(m +

If a point divides a segment

If a point divides a segment in the ratio 1:1, then it is the midpoint. So the coordinates of the midpoint of A(x1,y1) and B(x2,y2) are \left((x1 + x2