Sign In
To find the circumcenter, find the intersection of two perpendicular bisectors of two sides of the triangle.
(0,-1)
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 WX is horizontal, any perpendicular line will be vertical. Similarly, since XY is vertical, any perpendicular line will be horizontal. Let's find their midpoints. To do so, we can use the Midpoint Formula.
Side | Points | M(x_1+x_2/2,y_1+y_2/2) | Midpoint |
---|---|---|---|
WX | ( -1,4), ( 1,4) | A(-1+ 1/2,4+ 4/2) | A(0,4) |
XY | ( 1,4), ( 1,-6) | B(1+ 1/2,4+( -6)/2) | B(1,-1) |
Let's add these midpoints to our graph.
Given the information, we know that the perpendicular bisectors through WX and XY have the equations x=0 and y=-1, respectively.
The triangle's circumcenter is the point at which the perpendicular bisectors intersect.
We can see that the circumcenter is located at (0,-1).