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# URGENT Help!! Coordinate Geometry - rhombus watch

1. 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.
2. (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.?
3. (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 ?
Attached Images

4. (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.
5. (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 ?
6. (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.
7. (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 being the x coordinate of whatever the letter is. I like to use this formula because I hate having to draw shapes
8. (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 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)
9. (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.
10. (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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