Chapter 1.3, Problem 47PPS

To determine

To find the coordinates of missing point.

Answer to Problem 47PPS

Hence, coordinates of C are $(1,6)$ .

Explanation of Solution

Given information:

  $A(-5,4),B(-2,5)$

B is the midpoint of $AC$ .

Formula used:

  $x_m^{}=\frac{x_1^{}+x_2^{}}{2}$ For x coordinate of midpoint.

  $y_m^{}=\frac{y_1^{}+y_2^{}}{2}$ For y coordinate of midpoint.

Calculation:

Let the coordinates of C be $(x_2^{},y_2^{})$

Let coordinates of A be $(x_1^{},y_1^{})$ and

Coordinates of C be $(x_m^{},y_m^{})$

According to question, B is the midpoint of $AC$

So for x coordinate of C ,

  $-2=\frac{-5+x_2^{}}{2}$ ,

Solving,

  $-2(2)=-5+x_2^{}$

Now,

  $-4+5=x_2^{}$

Hence, x coordinate of C is 1.

For y coordinate of C ,

  $5=\frac{4+y_2^{}}{2}$ ,

Solving,

  $5(2)=4+y_2^{}$

Now,

  $10-4=y_2^{}$

Hence, y coordinate of C is 6.

Hence, coordinates of C are $(1,6)$ .