# AS Midpoint Problem

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#1
Is anyone able to help with the below question? It's out of my workbook but working isn't shown and I'm a bit stuck:

The line segment CD has midpoint (1,2), gradient 3/4 and length 5. Find the coordinates of the end points C and D.

I'm ok with finding the midpoint from two co-ordinates but struggling in reverse?
Last edited by beachpanda; 1 week ago
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1 week ago
#2
(Original post by beachpanda)
Is anyone able to help with the below question? It's out of my workbook but working isn't shown and I'm a bit stuck:

The line segment CD has midpoint (1,2), gradient 3/4 and length 5. Find the coordinates of the end points C and D.

I'm ok with finding the midpoint from two co-ordinates but struggling in reverse?
Can you sketch it? It sounds like a right angled triangle where you know the hypotenuse(5) and the tan of the angle (3/4). Just find the opp and adj. The answer is related to a well known Pythagorean triple.
Last edited by mqb2766; 1 week ago
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#3
(Original post by mqb2766)
Can you sketch it? It sounds like a right angled triangle where you know the hypothesis (5) and the tan of the angle (3/4). Just find the opp and adj. The answer is related to a well known Pythagorean triple.
Yep that's helped see things a lot clearer, managed to get to the right answer. Thankyou v much!
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#4
There was also this question in the same section - guessing it's applying the same principles but struggling to see it as we're not given the length / I can't see how we know how far away A & B are from the midpoint?

The line segment between the points A(2a, a) and B(b, b+3) has a gradient of 2 and a midpoint of (4,5). Find the exact distance between A and B.
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1 week ago
#5
What equations in terms of a and b can you write down for the gradient and midpoint?
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#6
(Original post by mqb2766)
What equations in terms of a and b can you write down for the gradient and midpoint?
I used the midpoint formula to get try and solve point A like this, where I'd split the rise/run of the gradient into two. I'm a bit unsure about how to bring in gradient when we don't know the length of the line though?

Point A = (2a+0.5 , a+1) = (4,5)

2a + 0.5 = 4
a + 1 = 5

But these equations gave me different values for a
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1 week ago
#7
(Original post by bakeshenanigans)
Xxx

I hope your answer matches mine Can you pls delete? The aim is to provide hints not full working.
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1 week ago
#8
(Original post by beachpanda)
I used the midpoint formula to get try and solve point A like this, where I'd split the rise/run of the gradient into two. I'm a bit unsure about how to bring in gradient when we don't know the length of the line though?

Point A = (2a+0.5 , a+1) = (4,5)

2a + 0.5 = 4
a + 1 = 5

But these equations gave me different values for a
Just use the midpoint and get a and b? What are the equations.
Last edited by mqb2766; 1 week ago
1
#9
(Original post by mqb2766)
Just use the midpoint and get a and b? What are the equations.
Used the midpoint formula, substituted for the coordinates and solved simultaneously - managed to get to the right answer.

Thankyou so so much for your help!!
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1 week ago
#10
(Original post by beachpanda)
Used the midpoint formula, substituted for the coordinates and solved simultaneously - managed to get to the right answer.

Thankyou so so much for your help!!
No problem, remember the midpoint is just the average, so add and divide by 2.
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