Chapter 1.3, Problem 63PPS

To determine

To find the coordinates

Answer to Problem 63PPS

Coordinates of B are $(-1.5,1)$

Explanation of Solution

Given information:

  $A(-4,-5),D(6,11)$

Formula used:

  $x_m^{}=\frac{x_1^{}+x_2^{}}{2}$ for coordinates of x

  $y_m^{}=\frac{y_1^{}+y_2^{}}{2}$ for coordinates of y

Calculation:

To find the coordinates of B, find coordinates of C first,

Let the coordinates of C be $(x_m^{},y_m^{})$

Coordinates of A be $(x_1^{},y_1^{})$

Coordinates of D be $(x_2^{},y_2^{})$

Using midpoint formula,

  $x_m^{}=\frac{x_1^{}+x_2^{}}{2}$

Substituting values,

  $x_m^{}=\frac{-4+6}{2}$

So,

  $x_m^{}=1$

And,

  $y_m^{}=\frac{y_1^{}+y_2^{}}{2}$

Substituting values,

  $y_m^{}=\frac{-5+11}{2}$

So,

  $y_m^{}=3$

Hence coordinates of C are $(1,3)$

Now,

B is the midpoint of AC,

So now

Let the coordinates of B be $(x_m^{},y_m^{})$

Coordinates of A be $(x_1^{},y_1^{})$

Coordinates of C be $(x_2^{},y_2^{})$

Using midpoint formula,

  $x_m^{}=\frac{x_1^{}+x_2^{}}{2}$

Substituting values,

  $x_m^{}=\frac{-4+1}{2}$

So,

  $x_m^{}=-1.5$

And,

  $y_m^{}=\frac{y_1^{}+y_2^{}}{2}$

Substituting values,

  $y_m^{}=\frac{-5+3}{2}$

So,

  $y_m^{}=1$

Hence coordinates of B are $(-1.5,1)$ .