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