Question

Show that (0, 0) is equidistant from (1, 2), (-1, -2) and (2, 1).​

Answer 1

Step-by-step explanation:

1) if (0;0) if point A, (1;2) is point B; (-1;-2) is C, (2;1) is D, then

2) the vector AB is (1;2); vector AC is (-1;-2) and vector AD is (2;1), then

3) the length of AB, AC and AD are:

$|AB|=\sqrt{1^2+2^2}=\sqrt{5};$

$|AC|=\sqrt{(-1)^2+(-2)^2}=\sqrt{5};$

$|AD|=\sqrt{2^2+1^2}=\sqrt{5}.$

4) if the lengths above are equal, then it means that (0, 0) is equidistant from (1, 2), (-1, -2) and (2, 1).