Question

An artist is mapping out proposed new features for a triangular reflecting pool. She sketches the pool on grid paper. The coordinates of the vertices of the pool are (3, 3), (11, 3), and (3, −3). She wants to put a monument at the circumcenter of the pool. What are the coordinates of the monument?
A. (6, 1)
B. (5 2/3, 1)
C. (7, 0)
D. (3, 3)

Answer 1

Answer:

C. (7, 0)

Step-by-step explanation:

Circumcenter of a Triangle

The circumcenter is a point where all the tangent lines of the midpoints of the three sides meet.

The coordinates of the vertices of the pool are (3, 3), (11, 3), and (3, −3). Please refer to the image below where the three midpoints are also shown. Since the triangle is right and two of its sides are parallel to the x-axis and the y-axis, the coordinates of the midpoints are very easy to find

Midpoint of (3, 3), (11, 3)=([3+11]/2,[3+3]/2)=(7,3)

Midpoint of (3,3), (3,-3) =([3+3]/2,[3-3]/2)=(3,0)

The intersection of both lines (shown in red) is the point (7,0) which is also the midpoint of (3,-3), (11,3). Thus this point is where all the midpoints meet.

Answer: C. (7, 0)