Question 1011205
B is on a line with y=-2x+5
It is also on a line going through A with slope -3/4.  That is y-2=-(3/4)(x+1); y=(-3x/4)+5/4
Therefore, -2x+5=(-3x/4)+(5/4)
-(5x/4)=-15/4, and x=3, so y=-1 as you found 
Now you can compute the slope of BC, which is 1.
Therefore, AD has a slope of 1.
Equation of BC is y-1=(x-5) or y=x-4
Equation of AD is y-2=(x+1) or y=x+3. CD has a slope of (-3/4), and its equation is y-1=(-3/4)(x-5)
y=(-3x/4)+(15/4).  CD and AD intersect at D, so (-3x/4)+15/4= x+3
-7x/4=-3/4, and x=(3/7).  Therefore y=24/7
{{{graph(300,200,-10,10,-10,10,x-4,x+3,(-3x/4)+(15/4),(-3x/4)+2)}}}