Coordinate Geometry

If two points lie on

If two points lie on the X-axis, their distance is the absolute difference of their x-coordinates: distance = |x2 - x1|. If two points lie on the Y-ax

For points A(x1

For points A(x1, y1) and B(x2, y2), the distance formula is d = sqrt((x2 - x1)^2 + (y2 - y1)^2). It is derived using the Pythagorean theorem in a righ

The distance of a point P(x

The distance of a point P(x, y) from the origin is sqrt(x^2 + y^2). This is a special case of the distance formula when one point is (0, 0).

If point P divides the line

If point P divides the line segment joining A(x1, y1) and B(x2, y2) internally in the ratio m1:m2, then P = ((m1x2 + m2x1)/(m1 + m2), (m1y2 + m2y1)/(m

The midpoint of a line segment

The midpoint of a line segment is a special case of the section formula with ratio 1:1. For endpoints (x1, y1) and (x2, y2), the midpoint is ((x1 + x2