Wednesday, July 22, 2015

Precalculus, Chapter 1, Review Exercises, Section Review Exercises, Problem 4

a. Find the distance between the points $(-2,2)$ and $(1,4)$.

Using the Distance Formula,


$
\begin{equation}
\begin{aligned}

d =& \sqrt{(-2-1)^2 + (2-4)^2}
\\
d =& \sqrt{9+4}
\\
d =& \sqrt{13}

\end{aligned}
\end{equation}
$


b. Find the midpoint of the given points.

Using the Midpoint Formula,


$
\begin{equation}
\begin{aligned}

M = (x,y) =& \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\\
\\
=& \left( \frac{-2+1}{2}, \frac{2+4}{2} \right)
\\
\\
=& \left( \frac{-1}{2}, 3 \right)

\end{aligned}
\end{equation}
$


c. Find the slope of the line containing the given points.

Using the Formula for Slope,


$
\begin{equation}
\begin{aligned}

m =& \frac{y_2- y_1}{x_2 - x_1}
\\
\\
=& \frac{4-2}{1-(-2)}
\\
\\
=& \frac{6}{3}
\\
\\
=& 2

\end{aligned}
\end{equation}
$


d. Interpret the slope in part (c).

For every increment of $x$ by 1 unit, $y$ will increase by 2 units.

No comments:

Post a Comment

Why is the fact that the Americans are helping the Russians important?

In the late author Tom Clancy’s first novel, The Hunt for Red October, the assistance rendered to the Russians by the United States is impor...