Question

find the coordinates of point h on \overline{ab} such that the ratio of ah to hb is 1:4

Explanation:

Step1: Find the coordinates of points A and B

From the graph, \(A=(0,0)\) and \(B=(3,6)\)

Step2: Use the section formula

If a point \(H(x,y)\) divides the line - segment joining \(A(x_1,y_1)\) and \(B(x_2,y_2)\) in the ratio \(m:n\), then the coordinates of \(H\) are given by \(x=\frac{mx_2 + nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here \(m = 1\), \(n = 4\), \(x_1=0\), \(y_1 = 0\), \(x_2=3\), \(y_2=6\)

Calculate \(x\) - coordinate

\(x=\frac{1\times3+4\times0}{1 + 4}=\frac{3+0}{5}=\frac{3}{5}=0.6\)

Calculate \(y\) - coordinate

\(y=\frac{1\times6+4\times0}{1 + 4}=\frac{6+0}{5}=\frac{6}{5}=1.2\)

Answer:

The coordinates of point \(H\) are \((0.6,1.2)\)