Question

What is the circumcenter of the triangle with vertices A(0,0) B(0,4) and C(8,0)

O (4,2)
O (2,4)
O (-2,3)
O (2,2)

Answer 1

The circumcenter of the triangle with vertices A(0,0), B(0,4), and C(8,0) is the point O (4,2), which is the midpoint of the hypotenuse BC.

Step-by-step explanation:

Finding the Circumcenter of a Triangle

To find the circumcenter of a triangle with vertices A(0,0), B(0,4), and C(8,0), we need to determine the point that is equidistant from all three vertices of the triangle. This point is where the perpendicular bisectors of the sides of the triangle intersect. In this case, the triangle is right-angled with the right angle at A since AB and AC are on the axes.

For a right-angled triangle, the circumcenter is located at the midpoint of the hypotenuse. Here, BC is the hypotenuse, so we find its midpoint. For B(0,4) and C(8,0), the midpoint M (the circumcenter) will have coordinates ((0+8)/2, (4+0)/2) = (4, 2).

• Coordinates of circumcenter: O (4,2)