Answer
$\color{blue}{\bf\text{(a) }\sqrt{29}}$
$\color{blue}{\bf\text{(b) }(\frac{3}{2},-1)}$
$\color{blue}{\bf\text{(c) }y=-\frac{2}{5}x-\frac{2}{5}}$
Work Step by Step
$\bf{(a)}$ distance between points $\bf{P(-1,0)}$ and $\bf{Q(4,-2)}$
Use the distance formula:
$$d=\sqrt{(x_2−x_1)^2+(y_2−y_1)^2}$$
$d(P,Q)=\sqrt{(-1−4)^2+(0−(-2))^2}$
$d(P,Q)=\sqrt{(-5)^2+2^2}$
$d(P,Q)=\sqrt{25+4}$
$d(P,Q)=\color{blue}{\bf\sqrt{29}}$
$\bf{(b)}$ midpoint between points $\bf{P(-1,0)}$ and $\bf{Q(4,-2)}$
Use the midpoint formula:
$$m=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$$
$m=(\frac{-1+4}{2},\frac{0+(-2)}{2})$
$m=(\frac{3}{2},-\frac{2}{2})$
$m=\color{blue}{(\bf\frac{3}{2},-1)}$
$\bf{(c)}$ equation for the line that passes through the points $\bf{P(-1,0)}$ and $\bf{Q(4,-2)}$ in slope intercept form
Use point slope form, $y−y_1=m(x−x_1)$
where $\bf{m}$ = slope = $\frac{\Delta{y}}{\Delta{x}} =\frac{y_1−y_2}{x_1−x_2}$
$$y−y_1=\frac{y_1−y_2}{x_1−x_2}(x−x_1)$$
$y−0=\frac{0-(-2)}{-1-4}(x−(-1))$
$y=-\frac{2}{5}(x+1)$
$5y=-2(x+1)$
$5y=-2x-2$
$\color{blue}{\bf{y=-\frac{2}{5}x-\frac{2}{5}}}$
$\color{blue}{\bf\text{(a) }\sqrt{29}}$
$\color{blue}{\bf\text{(b) }(\frac{3}{2},-1)}$
$\color{blue}{\bf\text{(c) }y=-\frac{2}{5}x-\frac{2}{5}}$
