What is section formula explain?

The section formula tells us the coordinates of the point which divides a given line segment into two parts such that their lengths are in the ratio m : n m:n m:n. The midpoint of a line segment is the point that divides a line segment in two equal halves.

How is section formula derived?

Section formula can be derived by constructing two right triangles and by using AA similarity. We find the ratio of the length of the sides of the triangle in terms of the given ratios, and then, on solving for x, and y, we can find the coordinates of the point that is dividing the line segment.

What is section formula example?

Answer: The section formula helps in determining the coordinates of a point which facilitates division of the line joining two points in a ratio. This takes place either internally or externally. P ( x , y ) = ( c ⋅ m + a ⋅ n m + n , d ⋅ m + b ⋅ n m + n ) .

How do you use the section 10 formula?

Section Formula.
Numerical: Find the coordinates of the point which divides the line segment joining the points (4, – 3) and (8, 5) in the ratio 3 : 1 internally.
Solution: Using section formula P(x, y) = { (m1x2 + m2x1)/(m1 + m2 ) , (m1y2 + m2y1)/(m1 + m2 ) }

What is Section Formula internally?

Let C (x, y) be a point which divides the line segment in the ratio of 3 : 1 i.e m : n = 3 : 1. Now using the formula C(x, y) = { (m × x2 + n × x1) / (m + n ) , (m × y2 + n × y1) / (m + n ) } as C is dividing internally.

What is internal section formula?

Let C (x, y) be a point which divides the line segment externally in the ratio of 4 : 3 i.e m : n = 4 : 3. Now using the formula C(x, y) = { (m × x2 – n × x1) / (m – n) , (m × y2 – n × y1) / (m – n ) } as C is dividing internally. value of x = (mx2 – nx1) / (m – n)

What is Section Formula externally?

External Section Formula When the point which divides the line segment is divided externally in the ratio m : n lies outside the line segment i.e when we extend the line it coincides with the point, then we can use this formula. It is also called External Division.

How do you find m1 and m2 in coordinate geometry?

Important Formulas:

The product of the slopes of two perpendicular lines is –1.
The slopes of two parallel lines are always equal. If m1 and m2 are slopes of two parallel lines, then m1=m2.
The distance between the points (x1, y1) and (x2, y2) is.