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

Question

asked Jun 19, 2023 29.6k views

1 Answer

Lodlock · Answer 1 · 2023-06-23T17:23:31+0000

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|=√(1^2+2^2)=√(5);

|AC|=√((-1)^2+(-2)^2)=√(5);

|AD|=√(2^2+1^2)=√(5).

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