Question

1.Find the coordinates of the point which divides the line segment joining the points (4,-3) and (8,5) in the ratio 3:1.​

Answer 1

(x,y)=(7,3)

Step-by-step explanation:

x=3(8)+1(4)/3+1, y=3(5)+1(-3)/3+1

x=7, y=3

Answer 2

Answer:

Coordinates of the point that divide the line segment  in the ratio of 3:1 is (7,3)

Step-by-step explanation:

( Note must know the section formula )

Let us consider the given line segment has two points on the Cartesian plane such that A has coordinates of (4,-3) and B has coordinates of (8,5). Notice that A has got a positive abscissa and a negative ordinate while B has both positive coordinates.

This implies point A lies in the 2nd Quadrant while point B in  the 1 st Quadrant.

______3___________:_________1______

A (4,-3)                            P(x,y)                        B (8,5)

Now let there be a point P(x,y) such that it divides the above line segment in the ratio 3 : 1 .

Now according to section formula we have --

$P(x,y) = [\frac{mx_{2} + n x_{1} }{m+n} , \frac{my_{2} +ny_{2} }{m+n} ]$

Based on the above data we have

m = 3

n = 1

x1 = 4

x2 = 8

y1 = -3

y2 = 5

Substituting the values in the equation we have-

$p(x,y)= [ \frac{3(8)+ 4}{3+1} ,\frac{3(5) -3}{3+1} ]\\ = [\frac{28}{4} ,\frac{12}{4} ]\\ = [7,3]$

On equating the coordinates we have

P(x,y) = P(7,3)

Thus, the coordinates of the point (P) that divides the given line segment in the ratio of 3 : 1 is (7,3) { abscissa = 7 while ordinate = 3} .

Thank you.