GeometryWatch

#1
A quadrilateral ABCD is formed by the points A(-3, 2), B(4, 3), C(9, -2) and D(2, -3).

a) Show that all four sides are equal in length.
b) Show that ABCD is not a square.

I have done part a. But for part b, how do I show it? I have no clue at all.

Thank you.
0
10 years ago
#2
Well, think about it. You have 4 sides of equal length, but it's not a square...What could the shape be like? What crucial thing will it not have?
Spoiler:
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Equal length sides + Right angle = square

How can you verify if it has such a thing?
Spoiler:
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Work out the gradients of BA and BC. How can you tell if they're at right angles?
Spoiler:
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Multiply them together

0
10 years ago
#3
If it's a square, then the angle between the lines will be 90 degrees, i.e. perpendicular. So if you show two of the lines which meet aren't perpendicular, then it's not a square.
#4
I see, thanks. If it is not a square but equal in length, what is it actually?

Thanks.
0
10 years ago
#5
Rhombus, I think it's called. Imagine pulling two opposite corners together.
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10 years ago
#6
I wouldn't do anything with gradients. Consider the lengths of the diagonals
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#7
(Original post by SimonM)
I wouldn't do anything with gradients. Consider the lengths of the diagonals
What can this show? Thanks.
0
10 years ago
#8
(Original post by Civ-217)
What can this show? Thanks.
What can you say about the two diagonals of any square? Is the same also true for a rhombus?
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