Question

point h lies on fg such that fh:gh is 3:1. graph h.

Explanation:

1. First, assume the coordinates of \(F=(x_1,y_1)\) and \(G=(x_2,y_2)\) from the graph. Let's say \(F=(3,17)\) and \(G=(9,9)\) (by observing the grid - points).

• 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 given by \(x=\frac{mx_2+nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here, \(m = 3\) and \(n = 1\).

1. Calculate the \(x\) - coordinate of \(H\):

• \(x=\frac{3\times9 + 1\times3}{3 + 1}=\frac{27+3}{4}=\frac{30}{4}=7.5\).

1. Calculate the \(y\) - coordinate of \(H\):

• \(y=\frac{3\times9+1\times17}{3 + 1}=\frac{27 + 17}{4}=\frac{44}{4}=11\).

1. To graph \(H\):

• Locate the point \((7.5,11)\) on the coordinate plane. Start at the origin, move 7.5 units to the right along the \(x\) - axis and 11 units up along the \(y\) - axis and mark the point \(H\).

Step1: Identify coordinates of \(F\) and \(G\)

Assume \(F=(3,17)\), \(G=(9,9)\)

Step2: Apply section - formula for \(x\) - coordinate

\(x=\frac{3\times9 + 1\times3}{3 + 1}\)

Step3: Simplify \(x\) - coordinate calculation

\(x=\frac{27+3}{4}=7.5\)

Step4: Apply section - formula for \(y\) - coordinate

\(y=\frac{3\times9+1\times17}{3 + 1}\)

Step5: Simplify \(y\) - coordinate calculation

\(y=\frac{27 + 17}{4}=11\)

Step6: Graph the point \(H\)

Locate \((7.5,11)\) on the plane

Answer:

Graph the point \((7.5,11)\) on the given coordinate plane.