Intersection 81611

Given a triangle ABC: A (-1,3), B(2,-2), C(-4,-3). Determine the coordinates of the intersection of the heights and the coordinates of the intersection of the axes of the sides.

Correct answer:

x1 =  -0.4545
y1 =  2.9091
x2 =  -1.2727
y2 =  -2.4545

Step-by-step explanation:

A=(1,3) B=(2,2) C=(4,3)  m1=BxAxByAy=2(1)(2)3=35=1321.6667 m2=BxCxByCy=2(4)(2)(3)=610.1667 m3=AxCxAyCy=(1)(4)3(3)=2  ABh1 M1=1/m1=1/(1.6667)=53=0.6 M2=1/m2=1/0.1667=6 M3=1/m3=1/2=21=0.5  h1:  (x1Cx)=M1 (y1Cy) (x1Ax)=M2 (y1Ay) (x1(4))=0.59999999999999 (y1(3)) (x1(1))=(5.9999999999999) (y13)  x10.6y1=2.2 x1+6y1=17  Row2Row1Row2 x10.6y1=2.2 6.6y1=19.2  y1=6.619.2=2.90909091 x1=2.2+0.59999999999999y1=2.2+0.6 2.90909091=0.45454545=0.4545  x1=1150.454545 y1=11322.909091   Verifying Solution:   T3=y1Byx1Bx=2.9091(2)(0.4545)2=21=0.5 T3=M3
s1=2Ax+Bx=2(1)+2=21=0.5 s2=2Ay+By=23+(2)=21=0.5  s3=2Bx+Cx=22+(4)=1 s4=2By+Cy=2(2)+(3)=25=221=2.5  s5=2Ax+Cx=2(1)+(4)=25=221=2.5 s6=2Ay+Cy=23+(3)=0  (x2s1)=M1 (y2s2) (x2s3)=M2 (y2s4) (x20.5)=0.59999999999999 (y20.5) (x2(1))=(5.9999999999999) (y2(2.5))  x20.6y2=0.2 x2+6y2=16  Pivot:Row1Row2 x2+6y2=16 x20.6y2=0.2  Row211 Row1Row2 x2+6y2=16 6.6y2=16.2  y2=6.616.2=2.45454545 x2=1165.9999999999999y2=1166 (2.45454545)=1.27272727=1.2727  x2=11141.272727 y2=11272.454545   Verifying Solution:  S3=y2s6x2s5=(2.4545)0(1.2727)(2.5)=21=0.5 S3=M3

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