Answer
(a) $2\sqrt{13}$ units
(b) $13$ units
(c) $4\sqrt2$ units
Work Step by Step
Recall:
The distance $d$ between the points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the distance formula:
$$d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$$
Use the formul above to find the distance beteween each pair of points:
(a) $d=\sqrt{(1-5)^2+(3-6)^2}=\sqrt{16+36}=\sqrt{52}=\sqrt{4(13)}=2\sqrt{13}$
(b) $d=\sqrt{(-2-3)^2+(0-12)^2}=\sqrt{25+144}=\sqrt{169}=\sqrt{13^2}=13$
(c) $d=\sqrt{(0-4)^2+(-4-0)^2}=\sqrt{16+16}=\sqrt{32}=\sqrt{16(2)}=4\sqrt2$
