Question

R(15 , 5) , T(9 , 20) and R-S-T. Find the ratio in which point S(11 , 15) divides seg RT.​

Answer 1

Answer:

The point S ( 11, 15 ) divides seg RT in the ratio 2 : 1.

Step-by-step-explanation:

NOTE: Refer to the attachment for the graphical representation.

The given points are

• R ( 15, 5 ) ≡ ( x₁, y₁ )
• T ( 9, 20 ) ≡ ( x,₂ y₂ )
• S ( 11, 15 ) ≡ ( x, y )

We have to find the ratio in which point S divides the seg RT.

Let the ratio be m : n.

Now, by section formula,

x = ( mx₂ + nx₁ ) / ( m + n )

⇒ 11 = ( m * 9 + n * 15 ) / ( m + n )

⇒ 11 ( m + n ) = 9m + 15n

⇒ 11m + 11n = 9m + 15n

⇒ 11m - 9m = 15n - 11n

⇒ 2m = 4n

⇒ m / n = 4 / 2

⇒ m / n = 2 / 1

⇒ m : n = 2 : 1

∴ The ratio in which point S divides seg RT is 2 : 1.

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We can find the ratio by using section formula for y coordinate too.

By section formula,

y = ( my₂ + ny₁ ) / ( m + n )

⇒ 15 = [ m * 20 + n * 5 ] / ( m + n )

⇒ 15 ( m + n ) = 20m + 5n

⇒ 15m + 15n = 20m + 5n

⇒ 15n - 5n = 20m - 15m

⇒ 10n = 5m

⇒ 5m = 10n

⇒ m / n = 10 / 5

⇒ m / n = 2 / 1

⇒ m : n = 2 : 1

∴ The ratio in which point S divides seg RT is 2 : 1.