Chapter 1.3, Problem 28E

To determine

To write: The equation for the lines connecting points A and C and points B and C.

Answer to Problem 28E

The equation of line connecting A and C is $y=-x+4$ , equation of line connecting B and C is $y=-x+4$

Explanation of Solution

Given Information: The given equation of line $y=x+4$ . Point C is at same distance from A and B.

The given equation $y=-x+4$

It is given point A lie on this line. Let A is the point where $x=0$

Therefore $y=-0+4=4$

A (0,4)

Let us consider B is the point where $y=0$

Therefore

  $\begin{array}{l}0=-x+4\\ x=4\end{array}$

B (4,0)

C is at same distance from A and B

C is mid-point of AB

  $\begin{array}{l}C=(\frac{0+4}{2},\frac{4+0}{2})\\ C=(2,2)\end{array}$

The equation of line connecting points A and C

  $m=\frac{2-4}{2-0}=\frac{-2}{2}=-1$

Slope of AC = -1

Now equation of AC

  $\begin{array}{l}y-y_1=m(x-x_1)\\ y-0=-1(x-4)\end{array}$

  $y=-x+4$

Slope of line connecting points B and C

Slope

  $=\frac{2-0}{2-4}=\frac{2}{-2}=-1$

Equation of BC

  $\begin{array}{l}y-4=-1(x-0)\\ y=-x+4\end{array}$

Thus, the equation of line connecting A and C is $y=-x+4$ , equation of line connecting B and C is $y=-x+4$