Chapter 13.4, Problem 3CE

a.

To determine

To explain, is $\overrightarrow{BC}$ parallel to $\overrightarrow{OD}$ .

Answer to Problem 3CE

From calculation part we get, $m_{OD}=m_{BC}$ parallel.

Explanation of Solution

Given information: The graph is.

  

Calculation: The required solution is obtained as,

slope $BC=\frac{y}{x}=\frac{4}{1}=4$

slope $OD=\frac{y}{x}=\frac{4}{1}=4$

Hence, from above $m_{OD}=m_{BC}$ parallel.

b.

To determine

To explain, Is $\overrightarrow{BC}=\overrightarrow{OD}$ .

Answer to Problem 3CE

From calculation part we get, $\overrightarrow{BC}=\overrightarrow{OD}$ .

Explanation of Solution

Given information: The graph is.

  

Calculation: The required solution is obtained as,

  $\begin{array}{l}\overrightarrow{BC}=\left(x_2-x_1,y_2-y_1\right)=\left(6-5,1-\left(-3\right)\right)=\left(1,4\right)\\ \overrightarrow{OD}=\left(x_2-x_1,y_2-y_1\right)=\left(1-0,4-0\right)=\left(1,4\right)\\ \overrightarrow{BC}=\overrightarrow{OD}\end{array}$

Hence, from the above solution $\overrightarrow{BC}=\overrightarrow{OD}$ .

c.

To determine

To explain the figure OBCD.

Answer to Problem 3CE

The figure OBCD is parallelogram.

Explanation of Solution

Given information: The graph is.

  

Calculation: The required solution is obtained as,

From figure,

  $\begin{array}{l}{m}_{OD}=m_{BC},\\ m_{OB}=m_{DC}\end{array}$

Hence, the figure OBCD is parallelogram.