Question

Line segment AB has endpoints A(1, 2) and B(5, 3). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:3.

Answer 1

Answer:

The coordinates of the point that divides the line segment directed from A to B in the ratio of 1:3 is P ( 2 , 2.25 ).

Step-by-step explanation:

Given:

Let Point P ( x , y ) divides Segment Am in the ratio 1 : 3 = m : n (say)

point A( x₁ , y₁) ≡ ( 1 , 2)

point B( x₂ , y₂) ≡ (5 , 3)  

To Find:

point P( x , y) ≡ ?

Solution:

IF a Point P divides Segment AB internally in the ratio m : n, then the Coordinates of Point P is given by Section Formula as

$x=\frac{(mx_{2} +nx_{1}) }{(m+n)}\\ \\and\\\\y=\frac{(my_{2} +ny_{1}) }{(m+n)}$

Substituting the values we get

$x=\frac{(1\times 5 +3\times 1) }{(1+3)}\\ \\and\\\\y=\frac{(1\times 3 +3\times 2) }{(1+3)}\\\\\therefore x = \frac{8}{4}=2 \\\\and\\\therefore y = \frac{9}{4}=2.25 \\\\\\\therefore P(x,y) = (2 , 2.25)$

The coordinates of the point that divides the line segment directed from A to B in the ratio of 1:3 is P ( 2 , 2.25 ).

Answer 2

Answer:

2, 9/4

Step-by-step explanation:

(2, 9/4)

(mx2 + nx1)

(m + n)

,

(my2 + ny1)

(m + n)

Where the point divides the segment internally in the ratio m:n

((1)(5) + (3)(1))

(1 + 3)

,

((1)(3) + (3)(2))

(1 + 3)

= 2,

9

4