Question

Line segment AB is divided by point P in the ratio of 1:4. Point A is (7,5) and point P is (10,14). What are the coordinates of point B?

Answer 1

Given:

The line segment AB is divided by point P in the ratio of 1:4.

Point A is (7,5) and point P is (10,14).

To find:

The coordinates of point B.

Solution:

Let the coordinates of point B are (a,b).

Section formula: If a point divide a line segment in m:n, then the coordinates of that point are

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

The line segment AB is divided by point P in the ratio of 1:4.

Using section formula, we get

$P=\left(\dfrac{1(a)+4(7)}{1+4},\dfrac{1(b)+4(5)}{1+4}\right)$

$(10,14)=\left(\dfrac{a+28}{5},\dfrac{b+20}{5}\right)$

Comparing the coordinates on both sides, we get

$\dfrac{a+28}{5}=10$

$a+28=50$

$a=50-28$

$a=22$

And,

$\dfrac{b+20}{5}=14$

$b+20=70$

$b=70-20$

$b=50$

Therefore, the coordinates of point B are (22,50).