section formula

 

. Section Formula (Internal Division)                      practice sums👈

• Used to find coordinates of a point dividing a line segment between two points in a given ratio.

• Let $A(x_1, y_1)$and $B(x_2, y_2)$ be two points.
  A point $P(x, y)$ divides $AB$in the ratio $m : n$.

• 🔸 Formula:

$$P(x, y) = \left( \frac{mx_2 + nx_1}{m + n},\ \frac{my_2 + ny_1}{m + n} \right)$$

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🔹 2. Midpoint Formula

• A special case of section formula when the ratio is 1:1 (i.e., the point divides the line segment in the middle).

• 🔸 Formula:

$$\text{Midpoint} = \left( \frac{x_1 + x_2}{2},\ \frac{y_1 + y_2}{2} \right)$$

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🔹 3. Centroid of a Triangle

• The centroid is the point of intersection of the medians of a triangle.

• If the vertices of the triangle are:
  $A(x_1, y_1),\ B(x_2, y_2),\ C(x_3, y_3)$
  

• 🔸 Formula:

$$\text{Centroid } G = \left( \frac{x_1 + x_2 + x_3}{3},\ \frac{y_1 + y_2 + y_3}{3} \right)$$