Chapter 3.3, Problem 50HP

To determine

The value of d .

Answer to Problem 50HP

  $d=\frac{c-a}{2}+b$

Explanation of Solution

Given:

The line passing through the points $\left(a,b\right)\text{ and }\left(c,d\right)$ has a slope $\frac{1}{2}$ .

Concept Used:

Equation of the line passing through the points $\left(x_1,y_1\right)\text{ and }\left(x_2,y_2\right)$ is given by $y-y_1=m\left(x-x_1\right)$ , where $\text{slope, }m=\frac{y_2-y_1}{x_2-x_1}$ .

Calculation:

The slope of any line is given by rise over run. That is, the ratio of the number of units it rise or fall over the number of units it move forward or backward from a fixed point.

Given that the line passing through the points $\left(a,b\right)\text{ and }\left(c,d\right)$ has a slope $\frac{1}{2}$ , so using the slope formula it gives

  $\begin{array}{c}\text{slope, }m=\frac{y_2-y_1}{x_2-x_1}\\ \frac{1}{2}=\frac{d-b}{c-a}\\ \frac{c-a}{2}=d-b\\ \frac{c-a}{2}+b=d\end{array}$

Thus, the value of d is given by $d=\frac{c-a}{2}+b$ .