anonymous
  • anonymous
show that the points K(2,4), L(4,2), M(2,-2) and N(-2,2) form the vertices of a trapezium
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
thanks..........
AkashdeepDeb
  • AkashdeepDeb
Do you know how to prove this is a quadrilateral?
anonymous
  • anonymous
Yes, I can help. Please wait while I go over your question.

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anonymous
  • anonymous
yes, a quadrilateral is just a 4 sided figure so by definition, 4 vertices make this a quadrilateral
anonymous
  • anonymous
but we need to show that this is a trapezium, right? I wouldn't say we need to prove it's a quadrilateral
anonymous
  • anonymous
because that is basically given they're asking to show it's a trapezium, right?
AkashdeepDeb
  • AkashdeepDeb
Okay @shree.gor ! As we have 4 points given already we know that it HAS to be a quadrilatral@ And to prove that it is a trapezium just find the slopes of all the sides! And 2 sides' slopes would be the same [Showing that they are parrallel] Thus, we get the required Quadrilateral with 1 pair parallel lines [A Trapezium] Got it? :D
anonymous
  • anonymous
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anonymous
  • anonymous
okay, we need to show this is a trapezium. A 4-sided flat shape with straight sides and NO parallel sides is defined as a Trapezium. the key is no parallel sides how do know if sides are parallel or not? it deals with the slope of the lines if the lines have the same slope then the are parallel so for this problem we need to show that the lines all have different slopes.
anonymous
  • anonymous
|dw:1377860997773:dw|
anonymous
  • anonymous
so, how do we find the slope of each line? let's start with line KL, what would we need to do to find the slope between K(2,4) and L(4,2)
anonymous
  • anonymous
|dw:1377861095515:dw|
anonymous
  • anonymous
I put the slope formula on the board, as you can see above. so lets say k is point 1 and L is point 2, we plug in the x's and y's from each and then simplify
anonymous
  • anonymous
|dw:1377861234549:dw|
anonymous
  • anonymous
|dw:1377861356323:dw|
anonymous
  • anonymous
so our first slope is -1. Now you can take a crack at the slope between points L and M using the same process. Good luck! :)
anonymous
  • anonymous
So basically, we find the slopes between each pair of points KL, LM, MN, NK and then compare them to see if any are equal if none are equal. This is a trapezium we use the formula for slope on the board to find each slope.

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