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
1 answer:
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
You might be interested in
Answer:
(a) 0.09
(b) 0.06
(c) 0.0018
(d) 0.9118
(e) 0.03
Step-by-step explanation:
Let <em>A</em> = boards have solder defects and <em>B</em> = boards have surface defects.
The proportion of boards having solder defects is, P (A) = 0.06.
The proportion of boards having surface-finish defects is, P (B) = 0.03.
It is provided that the events A and B are independent, i.e.
(a)
Compute the probability that either a solder defect or a surface-finish defect or both are found as follows:
= P (A or B) + P (A and B)
Thus, the probability that either a solder defect or a surface-finish defect or both are found is 0.09.
(b)
The probability that a solder defect is found is 0.06.
(c)
The probability that both defect are found is:
Thus, the probability that both defect are found is 0.0018.
(d)
The probability that none of the defect is found is:
Thus, the probability that none of the defect is found is 0.9118.
(e)
The probability that the defect found is a surface finish is 0.03.