Answer to Question #130309 in Analytic Geometry for Galata

Question

Find the distance between the following pair of points
A) (-1,0) and (3,0)
B) (1,-2) and (1,4)
C) (-2,3) and (2,0)
E) (a,a) and (-a,-a)
F) (a,b) and (-a,-b)

Answer 1

In all cases we use the formula for the distance $d[(x_1,y_1),(x_2,y_2)]=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.

A) $d=\sqrt{(3-(-1))^2+(0-0)^2}=\sqrt{4^2}=4.$

B) $d=\sqrt{(1-1)^2+(4-(-2))^2}=\sqrt{6^2}=6.$

C) $d=\sqrt{(2-(-2))^2+(0-3)^2}=\sqrt{25}=5.$

E) $d=\sqrt{(-a-a)^2+(-a-a)^2}=\sqrt{8a^2}=2\sqrt{2}a.$

F)

$d=\sqrt{(-a-a)^2+(-b-b)^2}=\sqrt{4a^2+4b^2}=\\ 2\sqrt{a^2+b^2}.$