Question

find the co-ordinates of the point P which bisects segment having co-ordinates (3,2) and (5,-2)​

Answer 1

Question:

Find the coordinates of the point P which bisects the segment having the endpoints coordinates as (3,2) and (5,-2).

Answer:

P(4,0)

Note:

• Section formula :

If the point O(x,y) divides the line segment joining the points A(x1,y1) and B(x2,y2) in ratio m:n internally ,then the coordinates of the point O is given by;

x = (mx2 + nx1)/(m + n)

y = (my2 + ny1)/(m + n)

• Corollary of section formula :

If the point O(x,y) bisects the line segment joining the points A(x1,y1) and B(x2,y2) , then the coordinates of the point O is given by;

x = (x1+x2)/2

y = (y1+y2)/2

Solution:

Let the end points of the segment be

A(3,2) and B(5,-2).

Let the point P(x,y) bisects the segment AB ,then the coordinates of the point P will be given by ;

x = (3+5)/2 = 8/2 = 4

y = {2+(-2)}/2 = (2-2)/2 = 0/2 = 0

Hence,

The required coordinates of point P is

(4,0) .

Answer 2

Answer:

Suppose the end point of the segment will be : A(3,2) or B(5,-2) .

Suppose the coordinates of point be P .

and P(x,y) bisects the AB segment.

x = (3+5)/2 = 8/2 = 4.

or

y = {2+(-2)}/2 = (2 - 2)/2 = 0/2 = 0.

Answer : 4 or 0