AS Midpoint Problem

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.

(edited 3 years ago)

Reply 2

OP

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!

Reply 3

OP

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.

Reply 4

What equations in terms of a and b can you write down for the gradient and midpoint?

Reply 5

OP

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

Reply 6

Original post by bakeshenanigans

Xxx

I hope your answer matches mine :smile:

Can you pls delete? The aim is to provide hints not full working.

Reply 7

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.

(edited 3 years ago)

Reply 8

OP

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!!

Reply 9