Question

find the coordinate of p if q is the midpoint of \\( \overline { p r } \\), \\( r = - 47 \\), and \\( q = 98 \\).

Explanation:

Step1: Use the mid - point formula

If \(Q\) is the mid - point of \(\overline{PR}\), then the mid - point formula is \(q=\frac{p + r}{2}\), where \(q\) is the coordinate of the mid - point, \(p\) is the coordinate of point \(P\), and \(r\) is the coordinate of point \(R\).
Given \(q = 98\) and \(r=-47\), we can substitute these values into the formula: \(98=\frac{p+( - 47)}{2}\).

Step2: Solve the equation for \(p\)

Multiply both sides of the equation \(98=\frac{p - 47}{2}\) by \(2\): \(2\times98=p - 47\).
So, \(196=p - 47\).
Then add \(47\) to both sides of the equation: \(p=196 + 47\).

Answer:

\(p = 243\)