The coordinates of the point which divides the line joining the points (7, 3) and (11, -3) in the ratio 2 : 3 is
Answers
Given : -
A point divides a line in the ratio of 2:3
The co-ordinates of the line are (7,3) & (11,-3)
Required to find : -
- Co-ordinates of the point which is dividing the line ?
Formula used : -
In order to solve this question we need to use the section formula .
SECTION FORMULA
Let the point which divides the line be P with co-ordinates (x,y)
This implies;
P(x,y)={([mx2+nx1])/(m+n) + ([my2+my1])/(m+n)}
Here,
x1,x2,y1&y2 are respectively the co-ordinates of the line
m & n are the ratios in which the line is divided
The above section formula can be simplified as;
P(x)={([mx2+nx1])/(m+n)}
P(y)={([my2+ny1])/(m+n)}
This enables us to find the co-ordinates of the point step by step .
Solution : -
A point divides a line in the ratio of 2:3
The co-ordinates of the line are (7,3) & (11,-3)
We need to find the co-ordinates of point which is dividing the line.
So,
Let the co-ordinates of the point which is dividing the line be (x,y)
However,
The points of the line be A&B .
This implies;
- A = (7,3) (x1,y1)
- B = (11,-3) (x2,y2)
And,
Ratio = 2:3
- m = 2 & n = 3
Substituting this values in the section formula;
p(x)={([2][11]+[3][7])/(2+3)}
p(x)={(22+21)/(5)}
p(x)={(43)/(5)}
Similarly,
p(y)={([2][-3]+[3][3])/(2+3)}
p(y)={(-6+9)/(5)}
p(y)={(3)/(5)}
Hence,
The co-ordinate of the point which divides the line AB is P([43]/[5] , [3]/[5])