Question

If the point P (6, 3) lies on the line segment joining points A (4, 2) and B (8,4), then ​

Answer 1

Answer:

1 : 1

Step-by-step explanation:

Correct Question :-

If the point P (6, 3) lies on the line segment joining points A (4, 2) and B (8,4), then ​find PA : PB.

Given,

P = (6 , 3)

A = (4 , 2)

B = (8 , 4)

To Find :-

PA : PB

How To Do :-

First  we need to Find the Value of PA by using distance formula and next we need to find the value of PB by distance formula and then we need the obtain the ratio of both the terms.

Formula Required :-

Distance Formula :-

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Solution :-

First let's find the value of PA :-

P = (6 , 3)

Let ,

x₁ = 6 , y₁ = 3

A = (4 , 2)

let,

x₂ = 4 , y₂ = 2

Substituting in distance formula :-

$PA=\sqrt{(4-6)^2+(2-3)^2}$

$=\sqrt{(-2)^2+(-1)^2}$

$=\sqrt{4+1}$

$\therefore PA = \sqrt{5}$

Lets find the value of PB :-

P = (6 , 3)

Let ,

x₁ = 6 , y₁ = 3

B = (8 , 4)

let,

x₂ = 8 , y₂ = 4

Substituting in distance formula :-

$PB=\sqrt{(8-6)^2+(4-3)^2}$

$=\sqrt{(2)^2+(1)^2}$

$=\sqrt{4+1}$

$\therefore PB=\sqrt{5}$

PA : PB = √5 : √5

= 1 : 1

∴ PA : PB = 1 : 1.