Question

point n lies on lm such that ln:mn is 4:5. graph n.

Explanation:

1. First, assume the coordinates of \(L=(x_1,y_1)\) and \(M=(x_2,y_2)\) from the graph. Let \(L=(6,19)\) and \(M=(14,2)\).

• The section - formula for a point \(N=(x,y)\) that divides the line - segment joining \(L(x_1,y_1)\) and \(M(x_2,y_2)\) 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 \(m = 4\) and \(n = 5\).

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

• Substitute \(x_1 = 6\), \(x_2 = 14\), \(m = 4\), and \(n = 5\) into the \(x\) - coordinate formula.
• \(x=\frac{4\times14 + 5\times6}{4 + 5}=\frac{56+30}{9}=\frac{86}{9}\approx9.56\).

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

• Substitute \(y_1 = 19\), \(y_2 = 2\), \(m = 4\), and \(n = 5\) into the \(y\) - coordinate formula.
• \(y=\frac{4\times2+5\times19}{4 + 5}=\frac{8 + 95}{9}=\frac{103}{9}\approx11.44\).

Answer:

The coordinates of point \(N\) are approximately \((9.56,11.44)\). To graph \(N\), locate the point on the coordinate - plane with these \(x\) and \(y\) values.