Straight Lines

The distance between A(x1

The distance between A(x1, y1) and B(x2, y2) is AB = sqrt((x2 - x1)^2 + (y2 - y1)^2). It comes from the right triangle formed by horizontal and vertic

If R divides the segment joining

If R divides the segment joining (x1, y1) and (x2, y2) internally in the ratio m:n, then R = ((m x2 + n x1)/(m + n), (m y2 + n y1)/(m + n)). When m =

The centroid of a triangle

The centroid of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3) is ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3). It is the simple average of the thr

The incentre is the intersection point

The incentre is the intersection point of any two internal angle bisectors. If the sides BC, CA, and AB have lengths a, b, and c respectively, then th

For vertices (x1

For vertices (x1, y1), (x2, y2), and (x3, y3), the area is (1/2)|x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|.