Chapter 11.1, Problem 78E

To determine

Tocalculate:coordinates of the endpoint of a line segment

Answer to Problem 78E

  $(7,16,12)$

Explanation of Solution

Given information:coordinates of the other endpoint and the midpoint are $(3,0,2),(5,8,7)$ respectively

Formula used:midpoint of line segment joining points $(a,b,c)$ and $(A,B,C)$ is given by $\left(\frac{a+A}{2},\frac{b+B}{2},\frac{c+C}{2}\right)$

Calculation:

Midpoint of line segment joining points $(a,b,c),(A,B,C)$ is equal to $\left(\frac{a+A}{2},\frac{b+B}{2},\frac{c+C}{2}\right)$

Coordinates of the other endpoint $(A,B,C)=(3,0,2)$

Coordinates of the midpoint $=(5,8,7)$

Let $(a,b,c)$ be the coordinates of the one endpoint.

So,

  $\begin{array}{l}\left(\frac{a+3}{2},\frac{b+0}{2},\frac{c+2}{2}\right)=(5,8,7)\\ \Rightarrow (a+3,b,c+2)=(10,16,14)\\ \Rightarrow (a,b,c)=(7,16,12)\end{array}$

Hence, $(7,16,12)$ denotes coordinates of the other endpoint.