Question

maps leila is walking from the park at point p to a restaurant at point r. she wants to stop for a break when the distance she has traveled and the distance she has left to travel has a ratio of 3:5. at which point should leila stop for her break? r(0, 4) p(10, 3)

Explanation:

Step1: Recall the section - formula

If a point $Q(x,y)$ divides the line - segment joining $P(x_1,y_1)$ and $R(x_2,y_2)$ in the ratio $m:n$, then $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $m = 3$, $n = 5$, $x_1=10$, $y_1 = 3$, $x_2=0$, and $y_2 = 4$.

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

$x=\frac{3\times0 + 5\times10}{3+5}=\frac{50}{8}=\frac{25}{4}=6.25$.

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

$y=\frac{3\times4+5\times3}{3 + 5}=\frac{12 + 15}{8}=\frac{27}{8}=3.375$.

Answer:

The point at which Leila should stop for her break is $(6.25,3.375)$