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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, āˆ’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)

Respuesta :

elcharly64

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, āˆ’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)

Ver imagen elcharly64