Question

the coordipales of the point which divides the line Segment
joining the points (4, -3) and (8.5) in the ratio 3:1
are a (3,7) (2,3) c (7,3) d (-3,-7)​

Answer 1

Answer:

The coordinates of the point dividing line segment are ( 7, 3 ).

Option c. ( 7, 3 )

Step-by-step-explanation:

Let the given points of a line segment be A and B.

• A ≡ ( 4, - 3 ) ≡ ( x₁, y₁ )
• B ≡ ( 8, 5 ) ≡ ( x₂, y₂ )

Let the point dividing the line segment in ratio 3 : 1 be P.

• P ≡ ( x, y )
• m : n = 3 : 1

Now, by section formula,

x = ( mx₂ + nx₁ ) / ( m + n ) & y = ( my₂ + ny₁ ) / ( m + n )

∴ x = ( 3 * 8 + 1 * 4 ) / ( 3 + 1 )

⇒ x = ( 24 + 4 ) / 4

⇒ x = 28 / 4

⇒ x = 7

And,

y = ( my₂ + ny₁ ) / ( m + n )

⇒ y = [ 3 * 5 + 1 * ( - 3 ) ] / ( 3 + 1 )

⇒ y = ( 15 - 3 ) / 4

⇒ y = 12 / 4

⇒ y = 3

∴ P ( x, y ) = ( 7, 3 )

∴ The coordinates of the point dividing line segment are ( 7, 3 ).