Chapter 1.5, Problem 5PSA

a.

To determine

To Find: The coordinate of B and C.

Answer to Problem 5PSA

Coordinates of B and C are 2 and 9 respectively.

Explanation of Solution

Given:

  

B and C trisect $\overline{AD}$

Concept Used:

If points trisects a line segment, it divided in three equal parts.

Calculation:

As here, B and C trisect $\overline{AD}$

Where $l\left(\overline{AD}\right)=16-\left(-5\right)=21\text{units}$

  $l\left(\overline{AB}\right)=l\left(\overline{BC}\right)=l\left(\overline{CD}\right)=7\text{units}$

Thus, the coordinates of B and C are 2 and 9 respectively.

Conclusion:

Coordinates of B and C are 2 and 9 respectively.

b.

To determine

To Calculate: The length of AC.

Answer to Problem 5PSA

Length of AC is 14 units.

Explanation of Solution

Given:

  

B and C trisect $\overline{AD}$

Concept Used:

If points trisects a line segment, it divided in three equal parts.

Calculation:

As here, B and C trisect $\overline{AD}$

Where $l\left(\overline{AD}\right)=16-\left(-5\right)=21\text{units}$

  $l\left(\overline{AB}\right)=l\left(\overline{BC}\right)=l\left(\overline{CD}\right)=7\text{units}$

  $\therefore l\left(\overline{AC}\right)=l\left(\overline{AB}\right)+l\left(\overline{BC}\right)=7\text{units + }7\text{units = }14\text{units}$

Thus, the length of AC is 14 units.

Conclusion:

Length of AC is 14 units.