Question

If A = (-1, -3) and B = (11, -8), what is the length of AB ?

Answer 1

For this problem, you need to know the distance formula, as that'll give you the length of the line segment.

$distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\ where\ you\ have\ points\ (x_{1},y_{1})\ and\ (x_{2},y_{2}).$

Using points A and B, the formula becomes:
$A=(x_{1},y_{1})=(-1,-3)\\B=(x_{2},y_{2})=(11,-8)\\x_{1}=-1\\x_{2}=11\\y_{1}=-3\\y_{2}=-8\\\\distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\\\\length\ of\ AB=\sqrt{(11-(-1))^{2}+((-8)-(-3))^{2}}\\\\ length\ of\ AB=\sqrt{(11+1)^{2}+(3-8)^{2}}\\\\length\ of\ AB=\sqrt{(12)^{2}+(-5)^{2}}\\\\length\ of\ AB=\sqrt{144+25}\\\\length\ of\ AB=\sqrt{169}\\\\length\ of\ AB=\pm 13$

Length cannot be negative, so the length of AB is 13.