Coordinate Geometry

Match the items on the right to the items on the left.

Distance between two points

A (x_{1}, y_{1})

and

B (x_{2}, y_{2})

The mid-point M, of the line segment joining two points

A (x_{1}, y_{1})

and

B (x_{2}, y_{2})

Let

A (x_{1}, y_{1})

and

B (x_{2}, y_{2})

be two distinct points such that point P(x, y) divides AB internally in the ratio m : n. Then coordinates of P

Let

A (x_{1}, y_{1})

and

B (x_{2}, y_{2})

be two distinct points such that point P(x, y) divides AB externally in the ratio m : n. Then coordinates of P

The coordinates of the centroid (G) of a triangle with vertices

A (x_{1}, y_{1})

B (x_{2}, y_{2})

and

C (x_{3}, y_{3})

|A B| = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}

(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})

(\frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n y_{1}}{m + n})

(\frac{m x_{2} - n x_{1}}{m - n}, \frac{m y_{2} - n y_{1}}{m - n})

(\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3})