Question

Find the coordinates of a point Con the line segment joining the points A(6,3) and
B(-4,5) such that AC =3/5 AB.

Answer 1

Answer:

Co-ordinates of 'C' = (0 , 21/5)

Step-by-step explanation:

Given,

A = (6 , 3)

B = (-4 , 5)

AC = 3/5 AB

To Find :-

Co-ordinates of 'C'

How To Do :-

Here they given a condition that 'AC = 3/5 AB'. SO we need to transpose AB to L.H.S and we need to find the value of 'AC/AB'. We can see the value  'A' divides AC and AB in the ratio. So we need to fid the value of 'CB' and we need to apply section formula and we need to find the co-ordinates of 'C'.

Formula Required :-

Section(internal division) formula :-

$(x,y)=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)$

Solution :-

Let , co-ordinate of 'C' be :- (x , y)

Given ,

AC = 3/5 AB

→ AC/AB = 3/5

AC : AB = 3 : 5

→ In line segment AB , 'C' is a point.

AC = 3x , AB = 5x

→ AC + CB = AB

3x + CB = 5x

CB = 5x - 3x

CB = 2x

→ AC : CB = 3x : 2x

= 3 : 2

∴ 'C' divides line segment 'AB' in the ratio '3 : 2'.

Substituting the values in the section(internal division) formula :-

m : n = 3 : 2

A = (6 , 3)

x_1 = 6 , y_1 = 3

B = (-4 , 5)

x_2 = -4 , y_2 5

$C=\left(\dfrac{3(-4)+2(6)}{3+2},\dfrac{3(5)+2(3)}{3+2}\right)$

$=\left(\dfrac{-12+12}{5},\dfrac{15+6}{5}\right)$

= (0/5 , 21/5)

= (0 , 21/5)

∴ Co-ordinates of 'C' = (0 , 21/5)