Chapter 13.2, Problem 5CE

a.

To determine

To tell whether given expression

  $y_2-y_1$

positive or negative.

Answer to Problem 5CE

The expression

  $y_2-y_1$

is negative.

Explanation of Solution

Given:

Below is the figure given

  

Calculation:

From the figure given , it can be said that the coordinates $\left(x_2,y_2\right)$ lies in fourth quadrant and $\left(x_1,y_1\right)$ lies in second quadrant. It means that $x_2$ and $y_1$ have positive values and $y_2$ and $x_1$ have negative values.

So , the value of expression $y_2-y_1$ is negative because the value of $y_2$ is negative and $y_1$ is positive which makes overall expression negative,

consider any coordinate say $\left(-1,1\right)$ in second quadrant and $\left(1,-2\right)$ in fourth quadrant

so ,

  $y_2-y_1=-2-\left(1\right)=-3$

Therefore, the expression

  $y_2-y_1$

is negative.

b.

To determine

To tell whether given expression

  $x_2-x_1$

positive or negative.

Answer to Problem 5CE

The expression

  $x_2-x_1$

is positive.

Explanation of Solution

Given:

Below is the figure given

  

Calculation:

From the figure given , it can be said that the coordinates $\left(x_2,y_2\right)$ lies in fourth quadrant and $\left(x_1,y_1\right)$ lies in second quadrant. It means that $x_2$ and $y_1$ have positive values and $y_2$ and $x_1$ have negative values.

So , the value of expression $x_2-x_1$ is positive because the value of $x_2$ is positive and $x_1$ is negative which makes overall expression positive,

consider any coordinate say $\left(-1,1\right)$ in second quadrant and $\left(1,-2\right)$ in fourth quadrant

so ,

  $x_2-x_1=1-\left(-1\right)=2$

Therefore, the expression

  $x_2-x_1$

is positive.

c.

To determine

To tell whether given expression

  $\frac{y_2-y_1}{x_2-x_1}$

positive or negative.

Answer to Problem 5CE

the expression

  $\frac{y_2-y_1}{x_2-x_1}$

is negative.

Explanation of Solution

Given:

Below is the figure given

  

Calculation:

From the figure given , it can be said that the coordinates $\left(x_2,y_2\right)$ lies in fourth quadrant and $\left(x_1,y_1\right)$ lies in second quadrant. It means that $x_2$ and $y_1$ have positive values and $y_2$ and $x_1$ have negative values.

So , the value of expression $x_2-x_1$ is positive because the value of $x_2$ is positive and $x_1$ is negative which makes overall expression positive

the value of expression $y_2-y_1$ is negative because the value of $y_2$ is negative and $y_1$ is positive which makes overall expression negative,

consider any coordinate say $\left(-1,1\right)$ in second quadrant and $\left(1,-2\right)$ in fourth quadrant

so ,

  $x_2-x_1=1-\left(-1\right)=2$

  $y_2-y_1=-2-\left(1\right)=-3$

  $\frac{y_2-y_1}{x_2-x_1}=\frac{-3}{2}$

Therefore, the expression

  $\frac{y_2-y_1}{x_2-x_1}$

is negative.