NONAME

Preston Y Hour 3 Second Quarter Project

Triangle ABC

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In order to find midpoint D and midpoint E, the average x and y values must be found of segments BA and AC.

Point D: x coordinate: **(-1+2) /2** //therefore// 1/2 = 0.5 y coordinate: **(-3+3) /2** //therefore// 0/2 = 0 = 0.5/0

Point E: x coordinate: **(2+5) /2** //therefore// 7/2 = 3.5 y coordinate: **(3+-1) /2** //therefore// 2/2 = 1 = 3.5/1

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The slopes of segments BA and AC must be found next, in order to find the slope of the perpendicular bisectors.

Slope of segment BA: (-1,-3) __- (2, 3)__ (-3,-6) Slope of segment AC: (2,3) __- (5,-1)__ 4/-3) y=-1/2x+b 0=-1/2(.5)+b 0=-1/4+b so: y=-1/2x+1/4 y=3/4x+b 1=3/4(7/2)+b 1=21/8+b so: y=3/4x-13/8 There are now two perpendicular bisectors that bisect sides BA and AC.
 * So the slope is 2/1 or 2**
 * So the slope is 4/-3 or -1.33**
 * Perpendicular Slopes:**
 * For D (0.5,0)**
 * For E (3.5,1)**

__**System of Equations**__ -1/2x+1/4=3/4x-13/8 -3/4x -3/4x -5/4x+1/4=-13/8 -1/4 -1/4 -5/4x=-15/8 -5/4x(-4/5)=-15/8(-4/5) =3/2 y=-1/2(3/2)+1/4 =-1/2 so: The coordiates for the circumcenter (F) are (3/2,-1/2) _ __**Distance Formula**__ A (2,3) __- F (3/2,-1/2)__ 0.5, 3.5 The square root of (0.5)^2+(3.5)^2 = a radius of 3.535533906u

This is the final product with the circumcenter (F) at (3/2,-1/2) and the circumscribing circle