Answer
$\sqrt{(c-a)^2 + (d-b)^2}$; $10$
Work Step by Step
RECALL:
The distance $d$ between two points $(a, b)$ and $c, d)$ can be found using the distance formula:
$d=\sqrt{(c-a)^2 + (d-b)^2}$
Thus, using the formula above, the distance between the points $(1, 2)$ and $(7, 10)$ is:
$d=\sqrt{(7-1)^2+(10-2)^2}
\\d=\sqrt{6^2+8^2}
\\d=\sqrt{36+64}
\\d=\sqrt{100}
\\d=\sqrt{10^2}
\\d=10$
Thus, the missing expressions in the given statements are (in order):
$\sqrt{(c-a)^2 + (d-b)^2}$; $10$
