Question

point g lies on ef such that eg:fg is 3:5. graph g.

Explanation:

1. First, assume the coordinates of point \(E=(x_1,y_1)\) and point \(F=(x_2,y_2)\). From the graph, \(E = (- 10,6)\) and \(F=(7,-2)\).

• The section - formula for a point \(G=(x,y)\) that divides the line - segment joining \(E(x_1,y_1)\) and \(F(x_2,y_2)\) in the ratio \(m:n\) is given by:
• \(x=\frac{mx_2+nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\), where \(m = 3\) and \(n = 5\).

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

• Substitute \(x_1=-10\), \(x_2 = 7\), \(m = 3\), and \(n = 5\) into the \(x\) - coordinate formula.
• \(x=\frac{3\times7+5\times(-10)}{3 + 5}=\frac{21-50}{8}=\frac{-29}{8}=-3.625\).

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

• Substitute \(y_1 = 6\), \(y_2=-2\), \(m = 3\), and \(n = 5\) into the \(y\) - coordinate formula.
• \(y=\frac{3\times(-2)+5\times6}{3 + 5}=\frac{-6 + 30}{8}=\frac{24}{8}=3\).

Answer:

The coordinates of point \(G\) are \((-3.625,3)\). To graph \(G\), locate the point \((-3.625,3)\) on the coordinate - plane. Mark a point on the grid where \(x=-3.625\) (between \(-3\) and \(-4\)) and \(y = 3\).