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    Hey guys so I just came across a question that I'm not to sure how to solve. So it gives 4 coordinates A(x,y) B(x,y) C(x,y) D(x,y) - [the x and y are given as values in the actual question] and says to work out the gradients and midpoints and therefore show that the quadrilateral is a rhombus?
    But which two points would I use to work out the gradients and midpoints? Would it be the opposite points when I draw it out ? Also after I find the coordinates and midpoint what do I do ?

    Please could someone kindly look at my attachment and give me steps on how to complete this, I don't mind if you put in some numerical values.
    I would really appreciate any help and thanks in advance to anyone who does.
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    (Original post by Aty100)
    Hey guys so I just came across a question that I'm not to sure how to solve. So it gives 4 coordinates A(x,y) B(x,y) C(x,y) D(x,y) - [the x and y are given as values in the actual question] and says to work out the gradients and midpoints and therefore show that the quadrilateral is a rhombus?
    But which two points would I use to work out the gradients and midpoints? Would it be the opposite points when I draw it out ? Also after I find the coordinates and midpoint what do I do ?

    Please could someone kindly look at my attachment and give me steps on how to complete this, I don't mind if you put in some numerical values.
    I would really appreciate any help and thanks in advance to anyone who does.
    Sketch the shape to get an idea of what you are doing.

    What is the definition of a rhombus.

    How can you use what you have to show the quadrilateral is a rhombus.?
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    (Original post by poorform)
    Sketch the shape to get an idea of what you are doing.

    What is the definition of a rhombus.

    How can you use what you have to show the quadrilateral is a rhombus.?
    So a rhombus is a quadrilateral whose sides are all equal. So how do I prove it is a rhombus and not a square ?
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    (Original post by Aty100)
    So a rhombus is a quadrilateral whose sides are all equal. So how do I prove it is a rhombus and not a square ?
    You can check if the gradients of two adjacent sides are perpendicular or not.
    Or, you can find the length of the diagonal.

    Edit: From the question it doesn't look like that is what they want, but you'll have to post the wording of the question for me to figure it out.
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    (Original post by EricPiphany)
    You can check if the gradients of two adjacent sides are perpendicular or not.
    Or, you can find the length of the diagonal.

    Edit: From the question it doesn't look like that is what they want, but you'll have to post the wording of the question for me to figure it out.
    Thanks,
    So I got that the two diagonals have the same midpoint so cross at the midpoint and one has a gradient of 3 and the other has -1/3 - multipling gives -1 and so the lines are perpendicular so it is a rhombus.
    Is that correct ?
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    (Original post by EricPiphany)
    You can check if the gradients of two adjacent sides are perpendicular or not.
    Or, you can find the length of the diagonal.

    Edit: From the question it doesn't look like that is what they want, but you'll have to post the wording of the question for me to figure it out.
    Oh sorry I forgot to add that bit. It gives 4 points and says to find the midpoints and gradients of the diagonals hence showing that it is a rhombus.
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    (Original post by Aty100)
    Oh sorry I forgot to add that bit. It gives 4 points and says to find the midpoints and gradients of the diagonals hence showing that it is a rhombus.
    Hi, in C1 coordinate geometry questions relating to shapes often come up and a lot of marks are usually given for finding the area. The most common shape is the triangle. Here is a formula you can use that will solve an area of any triangle given that you have the coordinates of the three vertices.

     Ax(By - Cy) + Bx(Ay - Cy) + Cx(By - Ay) / 2

    Ax being the x coordinate of whatever the letter is. I like to use this formula because I hate having to draw shapes
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    (Original post by MathsAndCompSci)
    Hi, in C1 coordinate geometry questions relating to shapes often come up and a lot of marks are usually given for finding the area. The most common shape is the triangle. Here is a formula you can use that will solve an area of any triangle given that you have the coordinates of the three vertices.

     Ax(By - Cy) + Bx(Ay - Cy) + Cx(By - Ay) / 2

    Ax being the x coordinate of whatever the letter is. I like to use this formula because I hate having to draw shapes
    This gave me 50/2 which is 25 but by doing base x height /2 I got 50?

    My coordinate are A(4,7) B(-2,5) C(3,-10)
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    (Original post by Aty100)
    Oh sorry I forgot to add that bit. It gives 4 points and says to find the midpoints and gradients of the diagonals hence showing that it is a rhombus.
    In that case I think you just have to show that the midpoints of the diagonals coincide and that their gradients are perpendicular. I think that is sufficient to prove that the shape is a rhombus.

    Edit: It seems to be true, have a look here http://www.mathopenref.com/rhombusdiagonals.html.
    You can show that two lines are perpendicular by showing that the product of their gradients is equal to -1.
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    (Original post by poorform)
    Sketch the shape to get an idea of what you are doing.

    What is the definition of a rhombus.

    How can you use what you have to show the quadrilateral is a rhombus.?
    Diagonals of a rhombus cross at right angles. Perhaps finding the gradients of those would show whether or not they were perpendicular.
 
 
 
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