Question

What point divides the directed line segment ​ AB¯¯¯¯¯ ​ ⁢ into a 3:4 ratio?

A. (4,​ 3)

B. (7,​ 3)

C. (9,​ 3)

D. (12,​ 3)

Answer 1

B. (7 , 3) is the correct answer

Answer 2

ANSWER

The point is

`(7,3).`

Step-by-step explanation


The formula for the internal division of a line segment in the ratio


`m:n`

is given by the formula,



`( (mx_2 + nx_1)/(m + n) , (my_2 + ny_1)/(m + n))`

From the graph,


`A(x_1,y_1) = A(1,3)`

and

`B(x_2,y_2) = B(15,3)`

We substitute these values into the formula to get,


`( (3 * 15+ 4 * 1)/( 3 + 4) , (3 * 3+ 4 * 3)/(3+ 4))`

We simplify this to get,


`( (45+ 4 )/( 3 + 4) , (9+ 12)/(3+ 4))`


`( (49 )/( 7) , (21)/(7))`


`( 7 , 3)`

The correct answer us B.