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 section - formula

The section - formula for a point \(Q(x,y)\) that divides the line - segment joining \(P(x_1,y_1)\) and \(R(x_2,y_2)\) in the ratio \(m:n\) is given by \(x=\frac{mx_2+nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here, \(m = 3\), \(n = 5\), \(x_1=10\), \(y_1 = 3\), \(x_2=0\), \(y_2 = 4\).

Step2: Calculate the \(x\) - coordinate of the point

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

Step3: Calculate the \(y\) - coordinate of the 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 \((6.25,3.375)\)