Grade 11

Analytical Geometry

Use algebra to describe geometric shapes — measure distances, find midpoints, write equations of lines and circles.

Distance and Midpoint

Given two points on the Cartesian plane, you can always find the exact straight-line distance between them using Pythagoras, and the midpoint using averaging.

Theorem
AB=(x2−x1)2+(y2−y1)2AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
Theorem
M=(x1+x22,  y1+y22)M = \left(\frac{x_1 + x_2}{2},\; \frac{y_1 + y_2}{2}\right)
Interactive — drag A and B
Try it yourself
Loading…
Worked Example

Given A(−2, 3) and B(4, −1), find AB and the midpoint M.

Worked Example

M(3, −1) is the midpoint of AB. If A = (1, 5), find B.