Question

calculate the distance between the points F = (-2,-9) and P = (-6,-1) in the Cartesian plane. Write the exact answer in radical form.

Answer 1

over 4 units, up 8 units
pythagas gives \(d^2=4^2+8^2\) so \(d=\sqrt{4^2+8^2}=\sqrt{16+64}=\sqrt{80}\)

Answer 2

simplest radical form we have \(80=16\times 5\) so
\[\sqrt{80}=\sqrt{16\times 5}=\sqrt{16}\times \sqrt{5}=4\sqrt{5}\]