We know that
A Parallelogram <span>is a flat shape with opposite sides parallel and equal in length
</span>
we have
<span>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)-----></span>m=(1-5)/(5+1)<span> ------> m=-4/6----> m=-2/3
dAB=</span>√[4²+6²----> dAB=√52 units
<span>
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=</span>(-2/3)x+2<span>
Step 3
with the equation of a line CD find the point D (x,2)
</span>y=(-2/3)x+2
<span>for y=2
</span>2=(-2/3)x+2---> (-2/3)x=0-------> x=0
<span>the point D is (0,2)
step 4
find the distance CD
</span>C(6,-2) D(0,2)
d=√[(2+2)²+(6)²]--------> d=√52
<span>so
dAB=dCD
step 5
</span>find the slope and the distance between point A and D
A(-1,5) D(0,2)<span>
m=(2-5)/(0+1)----> m=-3
d=</span>√[3²+1²]----> d=√10
<span>
step 6
</span>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
therefore
the figure is a Parallelogram
using a graph tool
see the attached figure
the answer is
the x coordinate of point D is 0
A Parallelogram <span>is a flat shape with opposite sides parallel and equal in length
</span>
we have
<span>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)-----></span>m=(1-5)/(5+1)<span> ------> m=-4/6----> m=-2/3
dAB=</span>√[4²+6²----> dAB=√52 units
<span>
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=</span>(-2/3)x+2<span>
Step 3
with the equation of a line CD find the point D (x,2)
</span>y=(-2/3)x+2
<span>for y=2
</span>2=(-2/3)x+2---> (-2/3)x=0-------> x=0
<span>the point D is (0,2)
step 4
find the distance CD
</span>C(6,-2) D(0,2)
d=√[(2+2)²+(6)²]--------> d=√52
<span>so
dAB=dCD
step 5
</span>find the slope and the distance between point A and D
A(-1,5) D(0,2)<span>
m=(2-5)/(0+1)----> m=-3
d=</span>√[3²+1²]----> d=√10
<span>
step 6
</span>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
therefore
the figure is a Parallelogram
using a graph tool
see the attached figure
the answer is
the x coordinate of point D is 0