Chapter 8.1, Problem 5PSA

To determine

To Calculate:The slope of line AC using coordinate of point A and B.

Answer to Problem 5PSA

Slope of the line AC is $-\frac{1}{2}$

Explanation of Solution

Given information Coordinates of two points A ( − 5, 5) and B (3, 1)

Formula used Slope of the given line = $\frac{y_2-y_1}{x_2-x_1}$ , where coordinates of points are $\left(x_1,x_2\right)\&\left(y_1,y_2\right)$

Calculation:

Coordinates of points A & B are: ( − 5, 5) and (3, 1)

**emsp; $\therefore$ Slope of the line AB =

  $\begin{array}{l}\frac{1-5}{3-(-5)}\\ =\frac{-4}{8}\\ =-\frac{1}{2}\end{array}$

b

To determine

To Calculate:The slope of line AC using coordinate of point Cand B.

Answer to Problem 5PSA

Slope of the AC is $-\frac{1}{2}$

Explanation of Solution

Given information Coordinates of two points B (3, 1) and C (13, − 4 )

Formula used Slope of the given line = $\frac{y_2-y_1}{x_2-x_1}$ , where coordinates of points are $\left(x_1,x_2\right)\&\left(y_1,y_2\right)$

Calculation Coordinates of points B & C are: (3, 1) and (13, − 4)

**emsp; $\therefore$ Slope of the line AC =

  $\begin{array}{l}\frac{-4-1}{13-3}\\ =\frac{-5}{10}\\ =-\frac{1}{2}\end{array}$

c

To determine

To find:The answers of part a & b are same.

Answer to Problem 5PSA

Yes, they both are same

Explanation of Solution

Given information Part a: Slope of the AC , using coordinates of A & B is $-\frac{1}{2}$

Part b: Slope of the AC , using coordinates of B and C is $-\frac{1}{2}$

Formula used Slope of the given line = $\frac{y_2-y_1}{x_2-x_1}$ , where coordinates of points are $\left(x_1,x_2\right)\&\left(y_1,y_2\right)$

Calculation Part a: Slope of the AC , using coordinates of A & B is $-\frac{1}{2}$

Part b: Slope of the AC , using coordinates of B and C is $-\frac{1}{2}$

Yes, slopes are same, because line AC passes through A and B & B and C.