Question

point h lies on (overline{fg}) such that (fh:gh) is (3:1). graph h.

Explanation:

Step1: Assume coordinates of F and G

Let \(F=(x_1,y_1)=(6,17)\) and \(G=(x_2,y_2)=(18,9)\)

Step2: Use section - formula

The section formula for a point \(H=(x,y)\) that divides the line - segment joining \(F(x_1,y_1)\) and \(G(x_2,y_2)\) in the ratio \(m:n\) is \(x=\frac{mx_2+nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here \(m = 3\) and \(n = 1\)

For \(x\) - coordinate of \(H\):
\[x=\frac{3\times18+1\times6}{3 + 1}=\frac{54 + 6}{4}=\frac{60}{4}=15\]

For \(y\) - coordinate of \(H\):
\[y=\frac{3\times9+1\times17}{3 + 1}=\frac{27+17}{4}=\frac{44}{4}=11\]

So the coordinates of \(H\) are \((15,11)\)

Answer:

The point \(H\) has coordinates \((15,11)\) and can be graphed on the given coordinate - plane at the intersection of \(x = 15\) and \(y = 11\)