Question

x axis divide ratio joining line segment two points A(x1,y1)B(x2,y2) ratio formula proof​

Answer 1

Answer:

Section formula

Section Formula

When a point C divides a segment AB in the ratio m:n, we use the section formula to find the coordinates of that point. The section formula has 2 types. These types depend on the position of point C. It can be present between the 2 points or outside the segment.

The two types are:

Internal Section Formula

External Section Formula

Internal Section Formula

Also known as the Section Formula for Internal Division. When the line segment is divided internally in the ration m:n, we use this formula. That is when the point C lies somewhere between the points A and B. Understand the concept of Coordinate here.

The Coordinates of point C will be,

{[(mx2+nx1)/(m+n)],[(my2+ny1)/(m+n)]}

Breaking it down, the x coordinate is (mx2+nx1)/(m+n) and the y coordinate is (my2+ny1)/(m+n)

Section Formula for External Division

When the point P lies on the external part of the line segment, we use the section formula for the external division for its coordinates.

A point on the external part of the segment means when you extend the segment than its actual length the point lies there. Just as you see in the diagram above. The section formula for external division is,

P={[(mx2-nx1)/(m-n)],[(my2-ny1)/(m-n)]}

Breaking it down, the x coordinate is (mx2-nx1)/(m-n) and the y coordinate is (my2-ny1)/(m-n)

Understand the concept of Distance Formula here.

Midpoint Formula

When we need to find the coordinates of a point that lies exactly at the center of any given segment we use the midpoint formula.

The midpoint formula is,

P={(x1+x2)/2,(y1+y2)/2}

Breaking it down, the x-coordinate is (x1+x2)/2 and the y-coordinate is (y1+y2)/2