Chapter 9.1, Problem 42HP

To determine

To find: The coordinates of the point that is three fourths of the way from the given points.

Answer to Problem 42HP

The coordinates of the point that is three fourths of the way from the given points is $\left(3.5,-4.5\right)$

Explanation of Solution

Given:

The coordinates is given as,

  $P\left(-1,12\right)\text{ to }Q\left(5,-10\right)$

Calculation:

Let the midpoint be X and the A is the midpoint of X and Q.

  

The coordinates of the mid-point for PQ is calculated as,

  $\begin{array}{c}\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)=\left(\frac{-1+5}{2},\frac{12-10}{2}\right)\\ =\left(\frac{4}{2},\frac{2}{2}\right)\\ =\left(2,1\right)\end{array}$

The coordinates of the mid-point for XQ is calculated as,

  $\begin{array}{c}\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)=\left(\frac{2+5}{2},\frac{1-10}{2}\right)\\ =\left(\frac{7}{2},\frac{-9}{2}\right)\\ =\left(3.5,-4.5\right)\end{array}$

Thus, the coordinates of the point that is three fourths of the way from the given points is $\left(3.5,-4.5\right)$