Question

the coordinate of point x on $overline{pq}$ such that px to xq is 5:1 is

Explanation:

Step1: Identify the coordinates of P and Q

$P=-5$, $Q = 7$

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

The formula for finding the coordinate of a point $X$ that divides the line segment joining $P(x_1)$ and $Q(x_2)$ in the ratio $m:n$ is $X=\frac{mx_2+nx_1}{m + n}$. Here, $m = 5$, $n=1$, $x_1=-5$, $x_2 = 7$.
$X=\frac{5\times7+1\times(-5)}{5 + 1}$

Step3: Simplify the expression

First, calculate the numerator: $5\times7+1\times(-5)=35 - 5=30$.
Then, divide by the denominator: $\frac{30}{6}=5$.

Answer:

$5$