Chapter 7, Problem 26CCSR

a.

To determine

To calculate:Coordinates of the vertices of the tringle using algebraic methods to justify answers.

Answer to Problem 26CCSR

First vertex: $(1,2)$

Second vertex: $(8,2)$

Third vertex: $(3,4)$

Explanation of Solution

Given information:

  $\begin{array}{l}x-y=-1\\ y=2\\ -0.4x-y=-5.2\end{array}$

Calculation:

To find out the coordinates of tringles, lets solve the pair of equations turn by turn,

Let’s first solve equation first and second,

  $y=2$ ,

  $x-y=-1$ , $\therefore x=-1+y=-1+2=1$

First vertex: $(1,2)$

Now, let’s solve equation second and third,

  $y=2$ ,

  $-0.4x-y=-5.2$ , $\therefore x=\frac{-5.2+y}{-0.4}=8$

Second vertex: $(8,2)$

Now, let’s solve equation first and third,

  $x-y=-1$ , $\therefore y=x+1$

  $-0.4x-y=-5.2$ , $\therefore y=5.2-0.4x$

  $\therefore x+1=5.2-0.4x$

  $\therefore x=3$

  $\therefore y=x+1=4$

Third vertex: $(3,4)$

b.

To determine

To calculate:Draw a tringle. find out area of the triangle.

Answer to Problem 26CCSR

  

Area: 7 sq. units

Explanation of Solution

Given information:

  $\begin{array}{l}x-y=-1\\ y=2\\ -0.4x-y=-5.2\end{array}$

Calculation:

From the equations graph of a tringle is,

  

Now, the area of a tringle from the figure is,

Area = $\frac{1}{2}(2)(7)=7$ sq. units.