Question

the coordinates of the endpoints of $overline{no}$ are $n(5,7)$ and $o(13,15)$. point $p$ is on $overline{no}$ and divides it such that $np:op$ is $3:1$. what are the coordinates of $p$? write your answers as integers or decimals.

Explanation:

Step1: Recall the section - formula

If a point \(P(x,y)\) divides the line - segment joining \(N(x_1,y_1)\) and \(O(x_2,y_2)\) in the ratio \(m:n\), then \(x=\frac{mx_2+nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here, \(x_1 = 5,y_1 = 7,x_2 = 13,y_2 = 15,m = 3,n = 1\).

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

\[x=\frac{3\times13+1\times5}{3 + 1}=\frac{39 + 5}{4}=\frac{44}{4}=11\]

Step3: Calculate the \(y\) - coordinate of \(P\)

\[y=\frac{3\times15+1\times7}{3 + 1}=\frac{45+7}{4}=\frac{52}{4}=13\]

Answer:

\((11,13)\)