Question

find the point of intersection which divides the lines segment joining the A(7,-2) and B(1,-5) in ratio 7:2

Answer 1

Answer:

Point of intersection = (7/3 , -13/3)

Step-by-step explanation:

Given,

A = (7 , -2)

B = (1 , -5)

Ratio = 7 : 2

To Find :-

Point of Intersection.

How To Do :-

Here they given the value of co-ordinates of 'A' and 'B' and the ratio that point of intersection divides line segment AB. So we are asked to find the co-ordinates of point of intersection. So by using Internal division formula we need to find the value of co-ordinates of point of intersection.

Formula Required :-

Internal division :-

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

Solution :-

Ratio = m : n

7 : 2 = m : n

A = (7 , -2)

Let,

x_1 = 7 , y_1 = - 2

B = (1 , -5)

Let,

x_2 = 1 , y_2 = -5

Substituting in the formula :-

$Point\:of\:intersection=\left(\dfrac{7(1)+2(7)}{7+2},\dfrac{7(-5)+2(-2)}{7+2}\right)$

$=\left(\dfrac{7+14}{9},\dfrac{-35-4}{9}\right)$

= (21/9 , -39/9)

= (7/3 , -13/3)

∴ Point of intersection = (7/3 , -13/3).