Becca+B

Becca B Hour 3 Honors Geometry Quarter 2 Project



And so begins the story of the acute triangle. Here are its midpoints. Midpoint F= (-2+8)/2, (3+2)/2 Midpoint F= (3,2.5) Midpoint E: (6+8)/2, (7+2)/2 Midpoint E: (7, 4.5) This one-of-a-kind triangle's slopes were discovered by an American Geometry Student-Becca B. Slope CA: (3-2)/(-2-8) Slope CA: (-1/10) Slope BC: (7-2)/(6-8)Slope BC: (-5/2)  **Perpendicular Bisector Equations:** Perpendicular Bisector of CA: y=m(x)+b 2.5=10(3)+b 2.5=30+b -30 -30 27.5=b //y=10(x)+-27.5// Perpendicular Bisector of BC: y=m(x)+b 4.5=2/5(7)+b 4.5=2.8+b -2.8 -2.8 1.7=b //y=2/5(x)+17/10// The circumcenter's coordinates are **(3.04, 2.92)** __**10x+-27.5=2/3x+1.7**__ +27.5 +27.5 10x=2/5x+29.2 -2/5x -2/5x 9.6x=29.2 9.6x/9.6 29.2/9.6 //x=73/24 (3.04)// **//...//** y=10(73/24)+-27.5 y=365/12+-27.5 y=35/12 (2.92) The radius from the circumcenter to the three poitns is 5.04, circumscribing the acute triangle.