Hello,
1)Let's call A=inter (4x-y-7=0, x+3y-31=0)
4x-y=7
x+3y=31
==>13x=52==>x=4
and y=4*4-7=9
A=(4;9)
2)Let's call B=inter (4x-y-7=0, x+5y-7=0)
4x-y=7
x+5y=7
==>21x=42
==>x=2 and y=4*2-7=1
B=(2,1)
3) Slope of BD: y=-x/3+31/3 ==> slope perpendicular=3
Line BD:y-1=3(x-2)==>y=3x+5
4) Slope AE: y=-x/5+7/5 ==>slope perpendicular=5
Line AE: y-9=5(x-4)==> y=5x-11
5) intersection (BD;AE):
y=5x-11
y=3x-5
==>2x=6==>x=3
and y=3*3-5=4
H=(3,4)
1)Let's call A=inter (4x-y-7=0, x+3y-31=0)
4x-y=7
x+3y=31
==>13x=52==>x=4
and y=4*4-7=9
A=(4;9)
2)Let's call B=inter (4x-y-7=0, x+5y-7=0)
4x-y=7
x+5y=7
==>21x=42
==>x=2 and y=4*2-7=1
B=(2,1)
3) Slope of BD: y=-x/3+31/3 ==> slope perpendicular=3
Line BD:y-1=3(x-2)==>y=3x+5
4) Slope AE: y=-x/5+7/5 ==>slope perpendicular=5
Line AE: y-9=5(x-4)==> y=5x-11
5) intersection (BD;AE):
y=5x-11
y=3x-5
==>2x=6==>x=3
and y=3*3-5=4
H=(3,4)