Chapter 1.3, Problem 50PPS

To determine

To find the coordinates of missing point.

Answer to Problem 50PPS

Hence, coordinates of A are $(12,-8)$ .

Explanation of Solution

Given information:

  $C(-6,-2),B(-3,-5)$

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 coordinates of A be $(x_1^{},y_1^{})$ and Coordinates of C be $(x_m^{},y_m^{})$

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

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

So for x coordinate of A ,

  $-3=\frac{x_1^{}+(-6)}{2}$ ,

Solving,

  $3(2)=x_1^{}-6$

Now,

  $6+6=x_1^{}$

Hence, x coordinate of A is 12.

For y coordinate of C ,

  $-5=\frac{y_1^{}+(-2)}{2}$ ,

Solving,

  $-5(2)=y_1^{}-2$

Now,

  $-10+2=y_2^{}$

Hence, y coordinate of A is -8.

Hence, coordinates of A are $(12,-8)$ .