Maths question-help!

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QuietKarlos

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I hope this worked but I had an online maths test and had this question which I couldn’t do. I’d like to know if anyone on this forum would know how to do question c. The test is already finished so I’m not cheating or anything just to clarify. I want to know the answer so if I get a similar question down the line I’ll know how to do it. Thanks.
 
I could write out the whole solution, but I thought it would be more fun for you (and educational) to see if you can work it out from a hint or two.

First hint: The diagonals of a rhombus are perpendicular.

(I assume that you solved parts a and b. Let me know if you need help on those.)
 
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Thanks for your reply and I’ve gotten a right angled triangle with 8 as it’s base now (triangle MBC) but how would I find another side or angle of it? You can give me another hint since it’s good practice if you want or tell me the answer, either suits! Thanks again, God Bless!
 
I don’t see a way to directly solve that right triangle. (There might be a way; I just don’t see it.)

Here is another hint: What do we know about the slopes of perpendicular lines?
 
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I think I have it:

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😃
 
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That’s correct.

I would have solved it along similar lines. (To solve such systems of equations, there are many trivial variations, and my work flow wouldn’t have been exactly the same.)

And speaking of variations, I ignored this part of the instructions of part c:

"Given that |BC| = |DC|"

That was a hint to use the distance formula:

|BC|2 = (x–2)2 + (12–10)2

|DC|2 = (x–6)2 + (12–2)2

Set these equal:

(x–2)2 + (12–10)2 = (x–6)2 + (12–2)2

Evaluate the squares and solve:

(x2 – 4x + 4) + 4 = (x2 – 12x + 36) + 100
…
x = 16

In retrospect, I think that’s what the examiner was looking for.
 
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In part d, the instruction “Hence or otherwise” suggests that you could similarly use the distance formulae, or use the symmetry of the rhombus to find p, the x coordinate of the opposite vertex.
 
Oh yes I tried to solve it at first using the distance formula but I did it very wrong. I’ll know how to do it in future though and that’s what’s important. Also they are very fun to do too!

And then the last one would just be 16 minus 4 and then 4 minus 12 is minus 8. Thanks very much again, God bless!
 
You’re welcome, God bless, and thank you for the interesting question.
 
somehow, even with the test over, I think it would be cheating if I stepped into this . . .
 
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