Chapter 1.3, Problem 48PPS

To determine

To find the coordinates of missing point.

Answer to Problem 48PPS

Hence, coordinates of C are $(5,-6)$ .

Explanation of Solution

Given information:

  $A(1,7),B(-3,1)$

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 C ,

  $-3=\frac{1+x_2^{}}{2}$ ,

Solving,

  $3(2)=1+x_2^{}$

Now,

  $6-1=x_2^{}$

Hence, x coordinate of C is 5.

For y coordinate of C ,

  $1=\frac{7+y_2^{}}{2}$ ,

Solving,

  $1(2)=7+y_2^{}$

Now,

  $1-7=y_2^{}$

Hence, y coordinate of C is -6.

Hence, coordinates of C are $(5,-6)$ .