Chapter 1.3, Problem 5BCYP

To determine

To find the coordinates of missing point.

Answer to Problem 5BCYP

Hence, coordinates of E are $(-7,0)$ .

Explanation of Solution

Given information:

  $P(-1,3),G(5,6)$

P is the midpoint of $EG$ .

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 E be $(x_2^{},y_2^{})$

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

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

According to question, P is the midpoint of $EG$

So for x coordinate of E ,

  $-1=\frac{5+x_2^{}}{2}$ ,

Solving,

  $-1(2)=5+x_2^{}$

Now,

  $-2-5=x_2^{}$

Hence, x coordinate of E is -7.

For y coordinate of E ,

  $3=\frac{6+y_2^{}}{2}$ ,

Solving,

  $3(2)=6+y_2^{}$

Now,

  $6-6=y_2^{}$

Hence, y coordinate of E is 0.

Hence, coordinates of E are $(-7,0)$ .