Find the coordinates of the point equidistant from the points A(1, 2), B (3, –4) and C(5, –6).a)(2, 3)b)(11, 2)c)(0, 3)d)(1, 3)Correct answer is option 'B'. Can you explain this answer?

Question

Find the coordinates of the point equidistant from the points A(1, 2), B (3, &ndash;4) and C(5, &ndash;6).a)(2, 3)b)(11, 2)c)(0, 3)d)(1, 3)Correct answer is option 'B'. Can you explain this answer?

Answer

4), and C(5, 6).

Let's call the unknown point (x, y). We know that it is equidistant from A, B, and C, which means that its distance to each point is the same.

Using the distance formula, we can write three equations:

(x - 1)^2 + (y - 2)^2 = (x - 3)^2 + (y - 4)^2
(x - 1)^2 + (y - 2)^2 = (x - 5)^2 + (y - 6)^2
(x - 3)^2 + (y - 4)^2 = (x - 5)^2 + (y - 6)^2

Expanding each equation and simplifying, we get:

-2x - 2y + 10 = 0
-4x - 4y + 20 = 0
-2x - 2y + 8 = 0

We can see that the first and third equations are equivalent, so we only need to solve the first two. We can use substitution:

-2x - 2y + 10 = 0
-2x - 2y + 10 = 0

Solving for y in the first equation, we get:

y = -x + 5

Substituting into the second equation, we get:

-4x - 4(-x + 5) + 20 = 0

Simplifying and solving for x, we get:

x = 3

Substituting x = 3 into y = -x + 5, we get:

y = 2

Therefore, the point equidistant from A, B, and C is (3, 2).

Answer

Could anybody plz tell me a different approach for this question

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