Question

If A (1, 2) and B (5, 6) are the coordinates of an equilateral triangle. Then what can we say about the abscissa of the third vertex?

• A. It is a positive integer
• B. It is an irrational number
• C. It is a negative integer
• D. 0
• E. Can’t say

Answer 1

The correct option is B

It is an irrational number

Given A (1, 2) and B (5, 6) are the coordinates of an equilateral triangle.

The third vertex will lie on the line on the perpendicular bisector of the line joining the two points.

Distance formula = $\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

Side length of the triangle = 4$\sqrt{2}$

Let the other point be P (x, y). ${(x-1)}^2+{(y-2)}^2$ = 32 ${(x-1)}^2+{(y-2)}^2$ = ${(x-5)}^2+{(y-6)}^2$.

Solving the two equations we get x = 3+2$\sqrt{3}$ or 3-2$\sqrt{3}$

So the abscissa of the other coordinate is an irrational number.