Question

Find the coordinates of the circumcenter of the triangle. D(0,0), E(6,0), F(0,4)

Answer 1

Answer:

in this question, we're going to be finding coordinates of the circumstance of a triangle, given the points, D. E. And F. So I'm going to explain this step by step, so that it's clear for you. Now, let's start, the first thing I want to do is to sketch just a plot to the different points. D. E. And F. So d. is at 00. The origin is at 60, And F is at 04. So that's the first step plotting out these points. Next uh I will join F. And E. So that we form the triangle that we're looking for. So the triangle D. E. F. He's actually uh a right triangle. Okay, no need to to do the other sides because you can see the triangle already, the triangle is D E. F. It's a right triangle. No, the second center is defined as the point where the perpendicular by sectors of the sides of a triangle intersect. So we want to draw a perpendicular lines. So the first perpendicular line we're going to draw is the one passing through the midpoint of the F. That's the perpendicular per sector of D. F. So I'm just going to draw it here. Um I'll use a different color, let me use green. So that's there. Fast, perpendicular by sector, Arabic, perpendicular by sector passes through the midpoint of aside and is passing also through an angle 90 degrees. Now let's draw the perpendicular by sector of D. E. So for D we also have to do the same thing, make sure that it passes through the midpoint And in this case the midpoint is at zero as 30. So I'm going to place this ruler at 30 after that is going to draw a line So far. You can see that these two uh will intersect at the .32. Now the midpoint of F. E. is also 32. Maybe we need to move this line slightly so that it's right where we wanted to be there. So 32, that's the point where these perpendicular by sectors meet, so The Sachem Center that has the .32