Question

Find the length of a segment with endpoints at (1,-2) and (-4,-4)

Answer 1

Call $(1,-2)$ for point A and $(-4, -4)$ for point B

Use the distance formula $AB = d(A, B) = \sqrt{(x_{B} - x_{A})^2 + (y_{B} - y_{A})^2}$

Insert values for $x_{B}$, $x_{A}$, $y_{B}$ and $y_{A}$

$AB = \sqrt{(-4 - 1)^2 + (-4 - (-2))^2}\\= \sqrt{(-4 - 1)^2 + (-4 + 2)^2}\\= \sqrt{(-5)^2 + (-2)^2}\\= \sqrt{25 + 4}\\= \sqrt{29}$