Question

If P(6,3)lies on the line segment joining points A(4,2) and B(8,4), then
(A) AP:PB=1:3
(B) AP: PB=1:4
(C) PB=PA
(D) AP: PB= 4:1

Answer 1

Option c is correct

c) PA = PB

Answer 2

Concept:

To determine the ratio in which a line segment is divided by a point inside or externally, apply the section formula. It is used to determine a triangle's centroid, incenter, and excenter. It is employed in physics to identify equilibrium locations, system centres of mass, etc.

x=(mx₂+nx₁)/(m+n)

y=(my₂+ny₁)/(m+n)

GIVEN:

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

FIND:

(A) AP:PB=1:3

(B) AP: PB=1:4

(C) PB=PA

(D) AP: PB= 4:1

SOLUTION:

Let there be two points A(4,2) and B(8,4)

P(6,3) dividing the line joining a nd B

Using section formula

x=(mx₂+nx₁)/(m+n)

y=(my₂+ny₁)/(m+n)

Let m:n=k:1

As per question:

x=(kx8+1x4)/(k+1)

⇒6=(kx8+1x4)/(k+1)

⇒6k+6=8k+4

⇒k=1

So, we can say P is the midpoint of AB and divides the line AB is the ratio 1:1

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