A level maths vectors help
Please help me with this question:
The points A, B, C, and D have coordinates (2a,b), (4a,2b), (3a-1,-b) and (a-1,-2b), respectively
b) For what values of a is ABCD a rhombus?
I did part a and got it correct (prove ABCD is a parallelogram), but I am confused about the second part. I found that vector AB is (2a / b) and the magnitude is sqrt(4a^2+b^2), and vector AD is (-a-1 / -3b ), which is different from the answer but I cannot figure out where I have gone wrong.
I did AD = -OA + OD = (-2a / -b) + (a-1 / -2b) = (-a-1 / -3b )
(I have not written the vectors as fractions but I don't know how else to type them)
The answer says that vector AD is (-a-1 / b )
Please help I don't know where I have gone wrong
The points A, B, C, and D have coordinates (2a,b), (4a,2b), (3a-1,-b) and (a-1,-2b), respectively
b) For what values of a is ABCD a rhombus?
I did part a and got it correct (prove ABCD is a parallelogram), but I am confused about the second part. I found that vector AB is (2a / b) and the magnitude is sqrt(4a^2+b^2), and vector AD is (-a-1 / -3b ), which is different from the answer but I cannot figure out where I have gone wrong.
I did AD = -OA + OD = (-2a / -b) + (a-1 / -2b) = (-a-1 / -3b )
(I have not written the vectors as fractions but I don't know how else to type them)
The answer says that vector AD is (-a-1 / b )
Please help I don't know where I have gone wrong
Reply 1
Original post
by creamy-hexPlease help me with this question:
The points A, B, C, and D have coordinates (2a,b), (4a,2b), (3a-1,-b) and (a-1,-2b), respectively
b) For what values of a is ABCD a rhombus?
I did part a and got it correct (prove ABCD is a parallelogram), but I am confused about the second part. I found that vector AB is (2a / b) and the magnitude is sqrt(4a^2+b^2), and vector AD is (-a-1 / -3b ), which is different from the answer but I cannot figure out where I have gone wrong.
I did AD = -OA + OD = (-2a / -b) + (a-1 / -2b) = (-a-1 / -3b )
(I have not written the vectors as fractions but I don't know how else to type them)
The answer says that vector AD is (-a-1 / b )
Please help I don't know where I have gone wrong
The points A, B, C, and D have coordinates (2a,b), (4a,2b), (3a-1,-b) and (a-1,-2b), respectively
b) For what values of a is ABCD a rhombus?
I did part a and got it correct (prove ABCD is a parallelogram), but I am confused about the second part. I found that vector AB is (2a / b) and the magnitude is sqrt(4a^2+b^2), and vector AD is (-a-1 / -3b ), which is different from the answer but I cannot figure out where I have gone wrong.
I did AD = -OA + OD = (-2a / -b) + (a-1 / -2b) = (-a-1 / -3b )
(I have not written the vectors as fractions but I don't know how else to type them)
The answer says that vector AD is (-a-1 / b )
Please help I don't know where I have gone wrong
I did so:
AD = D - A = [(a - 1), -2b)] - (2a, b)
I performed the subtraction:
1.
For the x-coordinate: (a - 1) - 2a = -a - 1
2.
For the y-coordinate: -2b - b = -3b
Since ABCD is a rhombus ==> condition = four sides with equal length. You have to confirm that ∣AB∣ = ∣AD∣ and that these match ∣BC∣ and ∣CD∣ as well.
This last calculation is complex.
Bye,
Sandro
(edited 1 year ago)
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