Maddie

Second Quarter Project
Triangle ABC

To calculate the midpoints D and E, I found the average x value and the average y value of AC and BC.

to find point E: x coordinate: ( 4 + -4) / 2 = 0/2 = 0 y coordinate: ( -2 + 4) / 2 = 2/2 = 1

to find point D: x coordinate: ( 6 + -4) / 2 = 2/2 = 1 y coordinate: ( 6 + 4) / 2 = 10/2 = 5



__work__ ( -4,4) ( 4 - -2) / ( -4 - 4) = 6 / -8 = -3 / 4 ( 4,-2) __answer__ -3 / 4 __work__ I found the opposite reciprocal of -3 / 4 __answer__ 4 / 3 __**slope of CB:**__ __work__ ( -4,4) ( 6 - 4) / ( 6 - -4) = 2 / 10 = 1 / 5 ( 6,6) __answer__ 1 / 5 __work__ I found the opposite reciprocal of 1 / 5 __answer__ -5 / 1 = -5
 * __slope of CA:__**
 * __slope of line in which E is located:__**
 * __slope of line in which D is located:__**

__**equation for line with E located on it:**__ slope: 4 / 3 y intercept: 1

equation: y = 4 / 3x + 1 __**equation for line with D located on it:**__ slope: -5 y intercept (work shown below): 10

y = -5x + b

plug in the coordinate (1,5)

5 = -5 (1) + b 5 = -5 + b +5 +5 10 = b

equation: y = -5x + 10

y = 4 / 3x + 1 y = -5x + 10
 * __Finding the circumcenter (where the two lines intersect) using system of equations:__**

__work (for finding x value)__ __work (for finding y value)__ 4 / 3x + 1 = -5x + 10 y = -5 ( 27 / 19 ) + 10 + 5x +5x y = -135 / 19 + 10 19 / 3x + 1 = 10 y = 55 / 19 = 2.89 +-1 +-1 ( 19 / 3x) / (19 / 3) = ( 9 ) / ( 19 / 3) x = 27 / 19 = 1.42 __F coordinate:__ ( 27 / 19, 55 / 19 ) or ( 1.42 , 2.89 )



__distance between F and C:__ //__work__// ( 27 / 19, 55 / 19) ( -4 , 4)
 * __Circumscribing the triangle by finding the distance from the circumcenter to each vertex (using the distance formula):__**

55 / 19 - 4 = -21 / 19 27 / 19 - -4 = 103 / 19

( -21 / 19 ) ( -21 / 19 ) = 441 / 361 ( 103 / 19) ( 103 / 19 ) = 10609 / 361

441 / 361 + 10609 / 361 = 11050 / 361

square root of ( 11050 / 361 ) = about 5.53 //__answer__// square root of ( 11050 / 361 ) or about 5.53 __distance between F and B__ //__work__// ( 27 / 19, 55 / 19 ) ( 6 , 6 )

6 - 55 / 19 = 59 / 19 6 - 27 / 19 = 87 / 19

(59 / 19) (59 / 19) = 3481 / 361 (87 / 19) (87 / 19) = 7569 / 361

3481 / 361 + 7569 / 361 = 11050 / 361

square root of ( 11050 / 361 ) = about 5.53 //__answer__// square root of ( 11050 / 361 ) = about 5.53

__distance between F and A__ //__work__// (27 / 19, 55 / 19) ( 4 , -2)

-2 - 55 / 19 = -93 / 19 4 - 27 / 19 = 49 / 19

( -93 / 19) ( -93 / 19) = 8649 / 361 (49 / 19) (49 / 19) = 2401 / 361

8649 / 361 + 2401 / 361 = 11050 / 361

square root of ( 11050 / 361 ) = about 5.53 //__answer__// square root of ( 11050 / 361 ) = about 5.53