FE Civil Exam Portal

Analytic Geometry Example

Easy DifficultyFE Mathematics and Statistics

Find the distance between two points and the coordinates of the midpoint of the segment joining them.

In the plane, the distance between points P_{1} (x_{1}, y_{1}) and P_{2} (x_{2}, y_{2}) is given by the Pythagorean formula. The midpoint of the segment is the average of the coordinates. d = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} M = (\frac{x _{1} + x _{2}}{2}, \frac{y _{1} + y _{2}}{2})

Two points in the x y -plane are A (1, 3) and B (5, 12) . Find: The distance between A and B The midpoint of segment AB

A = (1, 3) B = (5, 12)

d = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} d = (5 - 1)^{2} + (12 - 3)^{2} = 16 + 81 = 97 d \approx 9.85

M = (\frac{x _{1} + x _{2}}{2}, \frac{y _{1} + y _{2}}{2}) M = (\frac{1 + 5}{2}, \frac{3 + 12}{2}) = (3, 7.5)

(1) Distance d \approx 9.85 (2) Midpoint M = (\frac{1 + 5}{2}, \frac{3 + 12}{2}) = (3, 7.5)

d = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} M = (\frac{x _{1} + x _{2}}{2}, \frac{y _{1} + y _{2}}{2})