Question

the coordinates of the endpoints of gh are g(2, 7) and h(11, 16). point i is on gh and divides it such that gi:hi is 4:5. what are the coordinates of i? write your answers as integers or decimals.

Explanation:

Step1: Recall the section - formula

If a point \(I(x,y)\) divides the line - segment joining \(G(x_1,y_1)\) and \(H(x_2,y_2)\) in the ratio \(m:n\), then \(x=\frac{mx_2+nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here, \(x_1 = 2,y_1 = 7,x_2 = 11,y_2 = 16,m = 4,n = 5\).

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

\[x=\frac{4\times11+5\times2}{4 + 5}=\frac{44 + 10}{9}=\frac{54}{9}=6\]

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

\[y=\frac{4\times16+5\times7}{4 + 5}=\frac{64+35}{9}=\frac{99}{9}=11\]

Answer:

\((6,11)\)