Question

11 points for clear answer​

Answer 1

Answer:

Coordinates of point are (3/2,0)

Step-by-step explanation:

Let the ratio be k : 1

Using section formula, we get,

⇒ 0 = [1(-3) + k(7)/1 + k]

⇒ k = 3/7

⇒ k = 3 : 7

Also,

x = (m₂x₁ + m₁x₂)/(m₁ + m₂)

 = [1(3) + k(-2)]/[1 + k]

= [3 - 2 * 3/7]/[1 + 3/7]

= 3/2

Therefore,

∴ Coordinates of point are (3/2,0)

Hope it helps!

Answer 2

1) 3:7

2) (3/2, 0)

Step-by-step explanation:

Let the ratio be k : 1 .

Then by the section formula, the coordinates of the point which divides AB in the ratio k : 1 are

[ (-2k+3) / (k+1) , (7k - 3) / (k+1) ]

The point lies on x-axis, and we know that on the x-axis the ordinate is 0.

Therefore, (7k-3) / (k+1) = 0

=> 7k-3 = 0

=> 7k = 3

=> k = 3/7

=> k : 1 = 3 : 7

Putting the value of k = 3/7, we get point of intersection as

{ [ -2(3/7) + 3] ÷ (3/7)+1 , 0 }

=> { [(-6/7) + 3] ÷ (3/7) + 1 , 0 }

=> [(-6+21)/7 ÷ (3+7)/7 , 0 ]

=> [ 15/7 ÷ 10/7 , 0 ]

=> [ 15/10 , 0 ]

=> ( 3/2 , 0 ).