Cumulative Standards Review
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To find the circumcenter, find the intersection of two perpendicular bisectors of two sides of the triangle.
B
Let's start by graphing the triangle using the given coordinates.
By the Slopes of Perpendicular Lines Theorem, we know that horizontal and vertical lines are perpendicular. Since AC is horizontal, any line perpendicular to it will be vertical. Similarly, since BC is vertical, any line perpendicular to it will be horizontal. Let's use the Midpoint Formula to find their midpoints.
| Side | Points | M(x_1+x_2/2,y_1+y_2/2) | Midpoint |
|---|---|---|---|
| AC | ( -7,0), ( -3,0) | U(-7+( -3)/2,0+ 0/2) | U(-5,0) |
| CB | ( -3,0), ( -3,8) | V(-3+( -3)/2,0+ 8/2) | V(-3,4) |
Let's add these midpoints to our graph.
Given the information, we know that the perpendicular bisectors through AC and CB have the equations x=- 5 and y=4, respectively.
A triangle's circumcenter is the point at which the perpendicular bisectors intersect.
We can see that the circumcenter is located at (- 5,4). This corresponds to answer B.