Distance Formula — Chapter Summary

For points A(x1

For points A(x1, y1) and B(x2, y2), the distance is AB = \sqrt{(x2-x1)^2+(y2-y1)^2} = \sqrt{(x1-x2)^2+(y1-y2)^2}. The subtraction order does not matte

A right

A right-angled triangle is formed with AC as the difference of the abscissae and BC as the difference of the ordinates. Then AB^2 = AC^2 + BC^2, which

The distance of any point (x

The distance of any point (x, y) from the origin (0,0) is \sqrt{(x-0)^2+(y-0)^2} = \sqrt{x^2+y^2}.

A point on the x

A point on the x-axis is written as (x, 0) because its ordinate is zero. A point on the y-axis is written as (0, y) because its abscissa is zero.

Three points

Three points A, B and C are collinear if one distance equals the sum of the other two, such as BC + AC = AB.