Chapter 13, Problem 18CR

To determine

To find the coordinate of endpoint of the segment using midpoint and other end point

Answer to Problem 18CR

  $\text{R :}\left(-11,11\right)$

Explanation of Solution

Given,

Midpoint $\text{M:(0,5)}$

  $\text{S:(11,-1)}$

If ${\text{R:(x}}_{\text{1}}{\text{,y}}_{\text{1}}\text{)}$ and ${\text{S(x}}_2{\text{,y}}_2\text{)}$ , then

Coordinate of the midpoint of segment $\overline{\text{RS}}$ ,

  $\text{M : }\left(\frac{{\text{x}}_{\text{1}}+{\text{x}}_2}{2},\frac{{\text{y}}_{\text{1}}+{\text{y}}_2}{2}\right)$

Here, $\text{M:(0,5)}$ and $\text{S:(11,-1)}$

Let $\text{R:(x,y)}$ , then

Coordinate of the midpoint of segment $\overline{\text{RS}}$ ,

  $\text{ (0,5) = }\left(\frac{x+11}{2},\frac{y-1}{2}\right)$

  $\text{0 = }\frac{x+11}{2}$ and $\text{5 = }\frac{y-1}{2}$

  $\text{0 = }x+11$ and $\text{10 = }y-1$

  $x=-11$ and $y=11$

Therefore, coordinate of R is

  $\text{R :}\left(-11,11\right)$