Question

The two vertices of a triangle are B(-3,1) and C(2,-2). If the coordinates of the intersection point H of the three heights are (9/11, 4/11), try to find the coordinates of another vertex A.​

Answer 1

(3,4)

Explanation:

Find the equation of BH. (x+3)/(9/11+3)=(y-1)/(4/11-1)

(x+3)/(42/11)= (y-1)/(-7/11)

(x+3)*11/42= (y-1)*11/-7

x+3= -6(y-1)

x+3=-6y+6

y=-1/6x+1/2

m1=-1/6

AC: y=m2x+b

m1*m2=-1 (for perpendicular lines)

-1/6m2=-1

m2=6

-2=6*2+b

b=-14

y=6x-14

Find CH

(x-2)/(9/11-2)= (y+2)/(4/11+2)

(x-2)/(-13/11)= (y+2)/26/11

(x-2)*-11/13=(y+2)*11/26

(x-2)(-2)=y+2

-2x+4=y+2

y=-2x+2

m3=-2

AB: y=m4x+b

m3*m4=-1

-2*m4=-1

m4=0.5

Take the point B from AB

1=-3*0.5+b

b=2.5

y=0.5x+2.5

A is the point of intersection of two linesAB and AC

We have simultaneous equations

y=6x-14

y=0.5x+2.5

6x-14=0.5x+2.5

5.5x=16.5

x=3

y=6*3-14=4