Question

hasan is traveling from the bank to the post - office. the bank is located at (-6, 3) and the post - office is located at (-10, 7) on a coordinate grid map. hasan plans to stop for a break when the ratio of the distance he has traveled to the distance he has left to travel is 3:7. where should he take a break? write your answer as a decimal. hasan should take a break at ( )( ).

Explanation:

Step1: Recall the section - formula

If a point $P(x,y)$ divides the line - segment joining $A(x_1,y_1)$ and $B(x_2,y_2)$ in the ratio $m:n$, then $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $A(-6,3)$ is the starting - point (bank), $B(-10,7)$ is the ending - point (post - office), and the ratio $m:n = 3:7$.

Step2: Calculate the x - coordinate of the break - point

$x=\frac{3\times(-10)+7\times(-6)}{3 + 7}=\frac{-30-42}{10}=\frac{-72}{10}=-7.2$.

Step3: Calculate the y - coordinate of the break - point

$y=\frac{3\times7+7\times3}{3 + 7}=\frac{21 + 21}{10}=\frac{42}{10}=4.2$.

Answer:

$(-7.2,4.2)$