X-coordinate 81737

In triangle ABC, determine the coordinates of point B if you know that points A and B lie on the line 3x-y-5=0, points A and C lie on line 2x+3y+4=0, point C lies on the x-coordinate axis, and the angle at vertex C is right.

Correct answer:

Bx =  5.3333
By =  11

Step-by-step explanation:

A=(x,y) C=(z,0)  3 xy5=0 2 x+3 y+4=0  3xy=5 2x+3y=4  Row232 Row1Row2 3xy=5 3.67y=7.33  y=3.666666677.33333333=2 x=35+y=352=1  x=1 y=2  A=(1,2) B=(x,y) C=(z,0)  2 z+3 0+4=0  2z=4  z=24=2  z=2  A=(1,2) B=(x,y) C=(2,0)  AB2 = AC2  + BC2  (x1)2+(y+2)2 = (21)2+(0+2)2 + (2x)2 + (0y)2  6 x + 4 y  12 = 0  6 x1+4 y112=0 3x1y15=0  6 x1+4 y112=0 3 x1y15=0  6x14y1=12 3x1y1=5  Row263 Row1Row2 6x14y1=12 y1=11  y1=111=11 x1=612+4y1=612+4 11=5.33333333  x1=3165.333333 y1=11  Bx=Bx=x1=5.3333

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