Chapter 1, Problem 21SGR

To determine

To find the midpoint of XY

Answer to Problem 21SGR

(-27,16)

Explanation of Solution

Given information:

Coordinates of midpoint M (-4,8) and Y(19,0)

Formula used:

Mid-point $M(X,Y)$

For $X=\frac{x_1^{}+x_2^{}}{2}$ , For $Y=\frac{y_1^{}+y_2^{}}{2}$

Calculation: let the coordinates of midpoint M(-4,8) be X and Y

Also let the coordinates of Y be $x_{2,}^{}{y}_2^{}$

Substituting values in the formula

  $-4=\frac{x_1^{}+19}{2}$

Using cross multiplication

  $-8=x_1+19$

Subtracting nineteen both sides

  $x_1=-27$

Now for another coordinate of Y

Substituting values in the formula

  $8=\frac{y_1+0}{2}$

Using cross multiplication method

  $16=y_1$ Or $y_1=16$

Therefore missing coordinates are M(-27,16)