Question 1011205: The points A(-1,2) and C(5,1) are opposite vertices of a parallelogram ABCD. The vertex B lies on the line 2x + y = 5. The side AB is parallel to the line 3x + 4y = 8. Find the equations of the sides AD and CD.
Hi, I have no idea how to solve this question and the coordinate of D is not given but I worked out that the coordinate of B s (3,-1)
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 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
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