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
$(7,3).$

EXPLANATION


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

$m:n$

is given by the formula,


$( \frac{mx_2 + nx_1}{m + n} , \frac{my_2 + ny_1}{m + n})$

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,

$( \frac{3 \times 15+ 4 \times 1}{ 3 + 4} , \frac{3 \times 3+ 4 \times 3}{3+ 4})$

We simplify this to get,

$( \frac{45+ 4 }{ 3 + 4} , \frac{9+ 12}{3+ 4})$

$( \frac{49 }{ 7} , \frac{21}{7})$

$( 7 , 3)$

The correct answer us B.