Answer:
1. √74; 2. (24.5, 21.5)
Step-by-step explanation:
1. Distance
You could use the distance formula to calculate the length of PQ, but I prefer a visual approach, because it requires less memorization.
Draw a horizontal line from P and a vertical line from Q until they intersect at R (28, 19).
Then you have a right triangle PQR, and you can use Pythagoras' theorem to calculate PQ.
[tex]\begin{array}{rcl}PQ^{2} & = & PR^{2} + QR^{2}\\& = & 7^{2} + 5^{2}\\ & = & 49 + 25\\& = & 74\\PQ& = & \mathbf{\sqrt{74}}\\\end{array}\\\text{d(P,Q) = $\large \boxed{\mathbf{\sqrt{74}}}$}[/tex]
2. Midpoint of line
The coordinates of the midpoint are half-way between the x- and y-coordinates of the end points.
For the x-coordinate, the half-way point is
(21 + 28)/2 = 49/2 = 24.5
For the y-coordinate, the half-way point is
(19 +24)/2 = 43/2 = 21.5
The coordinates of the midpoint M are (24.5, 21.5).
