The population of the United States is approximately 3×10 8 people. The population of Germany is approximately 8×107 people. Whi
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Answer:
IS a parallelogram
Step-by-step explanation:
The slope formula for the slope of the line between points (x1, y1) and (x2, y2) is ...
m = (y2 -y1)/(x2 -x1)
The distance formula for the length of that same line is ...
d = √((x2 -x1)^2 +(y2 -y1)^2)
Here, you're asked to use each of these formulas 4 times, once for each side of the quadrilateral. I find it convenient to let a calculator or spreadsheet do the repetitive calculations. The result is attached.
The attachment shows that opposites sides have the same length and slope, so are parallel. The quadrilateral is a parallelogram. (The two points used in each calculation are the ones on the result line and the line immediately below. That is why point B is copied to the end of the list.)
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<em>Additional comments</em>
There are much simpler ways to prove the figure is a parallelogram. My favorite is to add the coordinates of the end points of the diagonals:
B +D = (-2+6, -9-3) = (4, -12)
C +E = (0+4, -5-7) = (4, -12)
These values being the same demonstrates the midpoints of the diagonals are coincident. That will only be the case if the quadrilateral is a parallelogram.
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If you must use slope and distance formulas, showing either pair of opposite sides is parallel and have the same length is sufficient to guarantee that the other two sides are also parallel and have the same length. That is, the calculations required in this problem only need to be applied to one pair of opposite sides. (Using a spreadsheet, it's not a lot of extra work to do the calculations for both pairs of opposite sides.)
The solution to the statement 4 + (-4) is correctly given by the third number line.
- The solution given by plot 1 is : (-4) + (-4) as both arrows points 4 units to the left.
- The solution given by plot 2 is : ( 4 + 4) as both arrows points 4 units to the right.
- The solution given by plot 3 is (4) + (-4) as one arrow points 4 units to the left and the other points 4 units to the right.
- The solution given by the plot 4 is (-4 + 8) as one arrow points 4 units to the left and the other points 8 units to the right.
Therefore, the Number line which shows the solution 4 + (-4) is the third number line.
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