Quadrilateral ABCD has a vertices A(-1,5) B(5,1) C(6,-2) D(x,2) what is the x coordinate to make ABCD a parallelogram
Accepted Solution
A:
we know that A Parallelogram is a flat shape with opposite sides parallel and equal in length
we have A(-1,5) B(5,1) C(6,-2) D(x,2)
step 1 find the slope and the distance between point A and B m=(y2-y1)/(x2-x1)----->m=(1-5)/(5+1) ------> m=-4/6----> m=-2/3 dAB=√[4²+6²----> dAB=√52 units
step 2 find the equation of the line CD parallel to the line AB and pass through the point C m=-2/3 (parallel lines have the same slope) point C (6,-2) y-y1=m*(x-x1)-------> y+2=(-2/3)*(x-6)----> y=(-2/3)x+4-2----> y=(-2/3)x+2
Step 3 with the equation of a line CD find the point D (x,2) y=(-2/3)x+2 for y=2 2=(-2/3)x+2---> (-2/3)x=0-------> x=0 the point D is (0,2)
step 4 find the distance CD C(6,-2) D(0,2) d=√[(2+2)²+(6)²]--------> d=√52 so dAB=dCD
step 5 find the slope and the distance between point A and D A(-1,5) D(0,2) m=(2-5)/(0+1)----> m=-3 d=√[3²+1²]----> d=√10
step 6 find the slope and the distance between point B and C B(5,1) C(6,-2) m=(-2-1)/(6-5)----> m=-3 d=√[3²+1²]----> d=√10 so the slope BC=slope AD the distance BC=distance AD