Question

2.) the coordinate of point x on pq such that px to xq is 5:1 is:

Explanation:

Step1: Identify the coordinates of P and Q

Let the coordinate of \(P=- 5\) and the coordinate of \(Q = 7\).

Step2: Use the section - formula for a one - dimensional line

The section formula for a point \(x\) that divides the line segment joining \(a\) and \(b\) in the ratio \(m:n\) is \(x=\frac{ma+nb}{m + n}\). Here, \(a=-5\), \(b = 7\), \(m = 5\), and \(n=1\).
\[x=\frac{5\times(-5)+1\times7}{5 + 1}\]

Step3: Calculate the value of x

First, calculate the numerator: \(5\times(-5)+1\times7=-25 + 7=-18\). Then, divide by the denominator: \(x=\frac{-18}{6}=-3\).

Answer:

\(-3\)