The diagonals bisect one another. The midpoint of is ?
Here's a question from a past paper which I have successfully attempted. My question is regarding part (iii). I have successfully figured out the co-ordinates by the following method:
Gradient of AD x Gradient of CD = -1
Is my method correct, considering I did get the right answer?
But is there another simpler method to do this which would save time during an exam.
No, I meant real value of the x-co-ordinates has not been given since we have to calculate that ourselves.
I have already gotten the correct values by using the method mentioned in my first post.
As stated I want someone to solve this part of the question with a different, possibly easier method.
I am not after the answer, I am looking for an alternate method.
I really don't see what method you used in your first post, but here's how I'd do it.
Plato already told you that the midpoint of BD is M(6, 6).
This means the y-coordinates of B and D are also 6.
This distance from B to D is 20 (found using distance formula)
Each individual segment of the diagonals measure 10 since they are bisected.
Using the distance formula, it is easy to determine the x-coordinates of B and D.
M(6, 6) -----> D(h, 6) = 10
The diagonals of a rectangle bisect each other.Code:| C(12,14) | o | * * | * * * * B o - + - - - - - - - o D * | * ------*-+-------*------------ *| * o A|(0,-2) |
The diagram shows a rectangle
We have: .
The diagonal is parallel to the -axis.
Explain why the -coordinate of is 6.
. . Hence, the midpoint of is the midpoint of
The midpoint of AC is: .
Therefore, and have a -coordinate of 6.
We have: .The -coordinate of is
Express the gradients of and in terms of h,.
Calculate the -coordinates of and
Since we have: .
You can see the working in the Soroban's post. That's exactly how I did it!
How did you get this with only the Y co-ordinates known for both? Did you get the distance of AC which should be equal to BD?This distance from B to D is 20 (found using distance formula)
Soroban, thanks for your post, but I've already used that method to solve this problem and already mentioned it in my first post that I am looking for alternative methods to solve it! Thanks nonetheless!