Coordinate Geometry (DP IB Applications & Interpretation (AI): HL): Revision Note

Basic coordinate geometry

How do I find the midpoint of two points?

• The midpoint of two points is the middle point

  • It lies on the line segment joining the two points together

  • It is the point that is equidistant from the two points

• The coordinates of the midpoint of $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ are $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$

  • It is just the average of the two coordinates

  • This is given in the formula booklet under the prior learning section

How do I find the distance between two points?

• The distance between two points is the length of the line segment joining them

• The length of the line segment between $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is $d=\sqrt{{\left(x_1-x_2\right)}^2+{\left(y_1-y_2\right)}^2}$

  • This is just an application of Pythagoras' Theorem

  • This is given in the formula booklet under the prior learning section

• The line segment between A and B is denoted [AB]

How do I find the gradient of the line segment between two points?

• The gradient of the line segment between $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is $m=\frac{y_2-y_1}{x_2-x_1}$

  • This is change in $y$ divided by the change in $x$

  • This is given in the formula booklet under the functions section