Question

the coordinates of the endpoints of $overline{st}$ are $s(10,2)$ and $t(17,16)$. point $u$ is on $overline{st}$ and divides it such that $su:tu$ is $2:5$. what are the coordinates of $u$? write your answers as integers or decimals.

Explanation:

Step1: Use the section - formula for x - coordinate

The formula for the x - coordinate of a point \(U(x,y)\) that divides the line segment joining \(S(x_1,y_1)\) and \(T(x_2,y_2)\) in the ratio \(m:n\) is \(x=\frac{mx_2+nx_1}{m + n}\). Here \(x_1 = 10\), \(x_2=17\), \(m = 2\), \(n = 5\). So \(x=\frac{2\times17+5\times10}{2 + 5}=\frac{34 + 50}{7}=\frac{84}{7}=12\).

Step2: Use the section - formula for y - coordinate

The formula for the y - coordinate of a point \(U(x,y)\) that divides the line segment joining \(S(x_1,y_1)\) and \(T(x_2,y_2)\) in the ratio \(m:n\) is \(y=\frac{my_2+ny_1}{m + n}\). Here \(y_1 = 2\), \(y_2=16\), \(m = 2\), \(n = 5\). So \(y=\frac{2\times16+5\times2}{2 + 5}=\frac{32+10}{7}=\frac{42}{7}=6\).

Answer:

\((12,6)\)