Chapter 6.2, Problem 6PSA

a

To determine

To calculate: The slope of AB

Answer to Problem 6PSA

Slope of the given line $\overline{\text{AB}}$ is $$$-\frac{1}{7}$

Explanation of Solution

Given information:

A given chord is a line segment joining two points on the circle, i.e., $\overline{\text{AB}}$ is the chord of circle with center O

Formula used:

Slope of line is given by $\frac{{\text{y}}_2-y_1}{{\text{x}}_2-{\text{x}}_1}$ , where $\left({\text{x}}_1,{\text{y}}_1\right)$ and $\left({\text{x}}_2,{\text{y}}_2\right)$ are the coordinates of points through which line or line segment passes.

Calculation:

Slope of line is given by $\frac{{\text{y}}_2-y_1}{{\text{x}}_2-{\text{x}}_1}$ , where $\left({\text{x}}_1,{\text{y}}_1\right)$ and $\left({\text{x}}_2,{\text{y}}_2\right)$

  $\therefore$ Slope of $\overline{\text{AB}}$ = $\frac{3-4}{4-(-3)}=-\frac{1}{7}$

b

To determine

To calculate: The slope of the AC

Answer to Problem 6PSA

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

Explanation of Solution

Given information:

A given chord is a line segment joining two points on the circle, i.e., $\overline{\text{AC}}$ is the chord of circle with center O

Formula used:

Slope of line is given by $\frac{{\text{y}}_2-y_1}{{\text{x}}_2-{\text{x}}_1}$ , where $\left({\text{x}}_1,{\text{y}}_1\right)$ and $\left({\text{x}}_2,{\text{y}}_2\right)$ are the coordinates of points through which line or line segment passes.

Calculation:

Slope of line is given by $\frac{{\text{y}}_2-y_1}{{\text{x}}_2-{\text{x}}_1}$ , where $\left({\text{x}}_1,{\text{y}}_1\right)$ and $\left({\text{x}}_2,{\text{y}}_2\right)$

  $\therefore$Slope of $\overline{\text{CD}}$ = $\frac{0-4}{5-(-3)}=-\frac{4}{8}=-\frac{1}{2}$