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sertanlavr [38]
3 years ago
9

What are the coordinates of the circumcenter of a triangle with vertices A(0,1), B(2, 1) , and C(2, 5) ?

Mathematics
2 answers:
muminat3 years ago
6 0

Answer: The coordinates of circumcenter is (1,3).

Explanation:

It is given that the triangle have vertices A(0,1), B(2, 1) , and C(2, 5).

The distance formula,

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

AB=\sqrt{(2-0)^2+(1-1)^2}=2

BC=\sqrt{(2-2)^2+(5-1)^2}=4

AC=\sqrt{(2-0)^2+(5-1)^2}=\sqrt{20}

Since,

(AC)^2=(AB)^2+(BC)^2

By pythagoras we can say that the given triangle is a right angle triangle and AC is the hypotenuse of the triangle.

The circumcentre of a right angle triangle is the midpoint of the hypotenuse.

Midpoint of AC,

\text{Midpoint of AC}=(\frac{0+2}{2}, \frac{1+5}{2})

\text{Midpoint of AC}=(\frac{2}{2}, \frac{6}{2})

\text{Midpoint of AC}=(1,3)

Therefore, the coordinates of circumcenter is (1,3).

neonofarm [45]3 years ago
3 0
The correct answer is 
(1, 3) 
you can verify it with
Circumcenter Calculator

http://calculator.tutorvista.com/circumcenter-calculator.html
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