Notes On Section Formula - CBSE Class 10 Maths
Section Formula: Given two end points of line segment A(x1, y1) and B (x2, y2) you can determine the coordinates of the point P(x, y) that divides the given line segment in the ratio m : n internally using Section Formula  given by $\left(\frac{\mathrm{\text{m}}{\text{x}}_{2}+\mathrm{\text{n}}{\text{x}}_{1}}{\mathrm{\text{m + n}}}\mathrm{\text{,}}\frac{\text{m}{\text{y}}_{2}\mathrm{\text{+ n}}{\text{y}}_{1}\mathrm{\text{}}}{\mathrm{\text{m + n}}}\right)$  .  Midpoint: The midpoint of a line segment divides it into two equal parts or in the ratio 1:1. The midpoint of line segment joining the points (x1, y1) and (x2, y2) is  . Median: The line joining the vertex to the midpoint of opposite side of a triangle is called Median. Centroid: Three medians can be drawn to a triangle and the point of concurrency of medians of a triangle is called Centroid denoted with G. If A(x1, y1), B(x2, y2) and C(x3, y3) are vertices of a triangle then its centroid G is given by $\left(\frac{{\text{x}}_{1}\text{}\mathrm{\text{+}}\text{}{\text{x}}_{2}\text{}\mathrm{\text{+}}\text{}{\text{x}}_{3}}{3}\text{,}\frac{{\text{y}}_{1}\text{}\mathrm{\text{+}}\text{}{\text{y}}_{2}\text{}\mathrm{\text{+}}\text{}{\text{y}}_{3}}{3}\right)$. The centroid of a triangle divides the median in the ratio 2:1.

Summary

Section Formula: Given two end points of line segment A(x1, y1) and B (x2, y2) you can determine the coordinates of the point P(x, y) that divides the given line segment in the ratio m : n internally using Section Formula  given by $\left(\frac{\mathrm{\text{m}}{\text{x}}_{2}+\mathrm{\text{n}}{\text{x}}_{1}}{\mathrm{\text{m + n}}}\mathrm{\text{,}}\frac{\text{m}{\text{y}}_{2}\mathrm{\text{+ n}}{\text{y}}_{1}\mathrm{\text{}}}{\mathrm{\text{m + n}}}\right)$  .  Midpoint: The midpoint of a line segment divides it into two equal parts or in the ratio 1:1. The midpoint of line segment joining the points (x1, y1) and (x2, y2) is  . Median: The line joining the vertex to the midpoint of opposite side of a triangle is called Median. Centroid: Three medians can be drawn to a triangle and the point of concurrency of medians of a triangle is called Centroid denoted with G. If A(x1, y1), B(x2, y2) and C(x3, y3) are vertices of a triangle then its centroid G is given by $\left(\frac{{\text{x}}_{1}\text{}\mathrm{\text{+}}\text{}{\text{x}}_{2}\text{}\mathrm{\text{+}}\text{}{\text{x}}_{3}}{3}\text{,}\frac{{\text{y}}_{1}\text{}\mathrm{\text{+}}\text{}{\text{y}}_{2}\text{}\mathrm{\text{+}}\text{}{\text{y}}_{3}}{3}\right)$. The centroid of a triangle divides the median in the ratio 2:1.

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