In a figure, the points A(2,6),B(-4,0), and C(4,0) appear tolie on a circle. a.

Question

In a figure, the points A(2,6),B(-4,0), and C(4,0) appear tolie on a circle. a. Find the equation of the perpendicular bisector of AB b. Find the equation of the perpendicular bisector of BC c. Find the equation of the perpendicular bisector of AC d. Find the circumcenter of triangle ABC, the point ofintersection of the three perpendicular bisectors. e. Why is the circumcenter equidistant from the vertices oftriangle ABC (use knowledge of perpendicular bisectors)? f. Do the points A,B,C lie on a circle?Explain. I will rate you lifesaver ASAP.Thanks! In a figure, the points A(2,6),B(-4,0), and C(4,0) appear tolie on a circle. a. Find the equation of the perpendicular bisector of AB b. Find the equation of the perpendicular bisector of BC c. Find the equation of the perpendicular bisector of AC d. Find the circumcenter of triangle ABC, the point ofintersection of the three perpendicular bisectors. e. Why is the circumcenter equidistant from the vertices oftriangle ABC (use knowledge of perpendicular bisectors)? f. Do the points A,B,C lie on a circle?Explain. I will rate you lifesaver ASAP.Thanks!

Explanation / Answer

A(2,6), B(-4,0)
MidAB((2-4)/2, (6+0)/2) = (-2/2, 6/2) = (-1,3)
After finding the midpoint, find the slope of the the segmentAB(rise/run = 6/6 = 1). Take the reciprocal of that slope, andreverse the sign (slope = 1, the reciprocal is -1). Plug thereciprocal into the equation y=mx+b (y=-x+b). Plug in the x and yvalues of your midpoint and find your y-int (y=-x+b -- 3=1+b --b=2). Your final equation is y=-1+2. B. Do the same as above C. Do the same as above D. Make all three equations equal to each other. and find theshared x-value. Plug in the x-value into any of the equations andfind the y-value. This is your point of intersection. E. See link, look under section titled: Circumcircles oftriangles - http://en.wikipedia.org/wiki/Circumcircle F. See abovelink

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