Question

Chapter : Distance Formulae

Show that the points (-5,2) , (-5 – 3), (2, -3) and (2, 2) are the vertices of a parallelogram. Is the parallelogram a rectangle?
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Answer 1

Answer:

distance = time upon speed

Step-by-step explanation:

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Answer 2

Question :-

Show that the points (-5,2) , (-5 – 3), (2, -3) and (2, 2) are the vertices of a parallelogram. Is the parallelogram a rectangle?

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Solution :-

Let, A, B, C, D denote the points (-5,2), (-5, -3) (2,-3) and (2,2) respectively.

Then,

AB² = {-5-(-5)} + {2-(-3)}²-0²+5² = 25

So, AB = 5

BC² = (-5-2)² + {-3-(-3)}² = (-7)² +0²= 49

So, BC = 7

CD² = (2-2)²+(-3-2)² = 0²+(-5)² = 25

So, CD = 5

DA² = {2-(-5)}²+(2-2)² = 7² +0² = 49

So, DA =7

So, AB =CD and BC = DA.

Therefore, ABCD is a parallelogram.

Again, AC² = (-5-2)² + {2−(−3)}² = (-7)² + (5)² = 74

So, AC = √74

and BD² = (-5-2)² + (-3-2)² = (-7)²+(-5)² = 74

So, BD = √74

So, AC = BD i.e., the diagonals of the parallelogram are equal and therefore, the parallelogram is a rectangle.

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