Straight lines Formula Sheet
1. Distance between the points P (x1, y1) and
Q (X2, Y2) is PQ = √(𝑥2 − 𝜘1 )2 + (𝑦2 − 𝑦1 )2
2. The coordinates of a points dividing the line
segment joining the points (x1, y1) and (x2, y2)
𝑚𝑥2 +𝑛𝑥1 𝑚𝑦2 +𝑛𝑦1
internally in the ratio m:n is ( , )
𝑚+𝑛 𝑚+𝑛
𝑚𝜘2 −𝑛𝑥1 𝑚𝑦2 −𝑛𝑦1
Externally in the ratio m:n is ( , )
𝑚−𝑛 𝑚−𝑛
𝑥1 +𝑥2 𝑦1 +𝑦2
3. Midpoint: ( , )
2 2
4. Area of the triangle whose vertices are (x1, y1),
(x2, y2) and (x3, y3)
1
|𝑥1 (𝑦2 − 𝑦3 ) + 𝑥2 (𝑦3 − 𝑦1 ) + 𝑥3 (𝑦1 − 𝑦2 )|
2
𝑦2 −𝑦1
5. Slope of a line: m = tanθ =
𝑥2 −𝑥1
6. If the line L1 is parallel to L2 then slope m1 = m2.
1. Distance between the points P (x1, y1) and
Q (X2, Y2) is PQ = √(𝑥2 − 𝜘1 )2 + (𝑦2 − 𝑦1 )2
2. The coordinates of a points dividing the line
segment joining the points (x1, y1) and (x2, y2)
𝑚𝑥2 +𝑛𝑥1 𝑚𝑦2 +𝑛𝑦1
internally in the ratio m:n is ( , )
𝑚+𝑛 𝑚+𝑛
𝑚𝜘2 −𝑛𝑥1 𝑚𝑦2 −𝑛𝑦1
Externally in the ratio m:n is ( , )
𝑚−𝑛 𝑚−𝑛
𝑥1 +𝑥2 𝑦1 +𝑦2
3. Midpoint: ( , )
2 2
4. Area of the triangle whose vertices are (x1, y1),
(x2, y2) and (x3, y3)
1
|𝑥1 (𝑦2 − 𝑦3 ) + 𝑥2 (𝑦3 − 𝑦1 ) + 𝑥3 (𝑦1 − 𝑦2 )|
2
𝑦2 −𝑦1
5. Slope of a line: m = tanθ =
𝑥2 −𝑥1
6. If the line L1 is parallel to L2 then slope m1 = m2.
