Question

point p lies on (overline{no}) such that (np:op) is (1:3). graph p.

Explanation:

1. First, assume the coordinates of \(O=(0,0)\) and \(N = (- 4,-8)\).

• The section - formula for a point \(P(x,y)\) that divides the line - segment joining \(N(x_1,y_1)\) and \(O(x_2,y_2)\) 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, \(m = 1\), \(n = 3\), \(x_1=-4\), \(y_1=-8\), \(x_2 = 0\), and \(y_2 = 0\).

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

• Substitute the values into the \(x\) - coordinate formula: \(x=\frac{1\times0 + 3\times(-4)}{1 + 3}\).
• First, calculate the numerator: \(1\times0+3\times(-4)=0 - 12=-12\).
• Then, calculate the denominator: \(1 + 3 = 4\).
• So, \(x=\frac{-12}{4}=-3\).

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

• Substitute the values into the \(y\) - coordinate formula: \(y=\frac{1\times0+3\times(-8)}{1 + 3}\).
• First, calculate the numerator: \(1\times0 + 3\times(-8)=0-24=-24\).
• Then, calculate the denominator: \(1 + 3 = 4\).
• So, \(y=\frac{-24}{4}=-6\).

Answer:

The coordinates of point \(P\) are \((-3,-6)\). To graph \(P\), start at the origin \((0,0)\), move 3 units to the left along the \(x\) - axis and 6 units down along the \(y\) - axis and mark the point.