Find the coordinates of the circumcenter of the triangle with the given vertices. D(-7,-1), E(-1,-1), F(-7,-9)

Answer 1

The circumcenter of a right angled triangle is at the center of the hypotenuse.

So graph the co-ordinates on the paper and find the length of the hypotenuse using Pythagoras theorem.

Now that you have the length of the hyp and the side of a triangle, you can find the co-ordinates to be (-4,-5)

Answer 2

Plot the 3 points on a graph. You will see that you have a right triangle.

Mark the midpoint of line EF, which is at (-4,-5). Then draw in the lines from this point to the midpoints of the other 2 lines. You can now see that the figure is made up of 3-4-5 right triangles, and that the circumcenter is at (-4,-5)

If in doubt why this is true, look up the definition of the circumcenter.

Answer 3

Graphing the points will help you visualize the triangle and notice that it t is a right triangle. I tried to do below for you, but i could not upload an image. Use desmos and graph the points and folow the directions. First you see the graphed triangle with the circumcenter which is the point of concurrency of the perpendicular bisectors.

The process: After graphing the points, find the mid points of the two legs and draw perpendicular lines (90 degree angled lines) that extend through the midpoints. The one ine is the perpendicular bisector of the horizontal leg and the other line is the perpendicular bisector of the vertical leg. One key noticing is that in a right triangle the circumcenter always falls on the hypotenuse at (-4,-5). The main function behind the circumcenter is that it provides a point that is equidistant from all vertices. The circumcenter represents the center of a circle that will go through all the vertices of the given triangle. Notice that the center is halfway down the hypotenuse. The distant from the center to the point (-1,-1) is also equidistant to the center of the triangle.