Math, asked by mahirsoni, 8 months ago

The coordinates of the point which divides the line joining the points (7, 3) and (11, -3) in the ratio 2 : 3 is

Answers

Answered by MisterIncredible
17

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])

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