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Equation of a line

I've been using Mathsbot, and I've seen this question repeatedly come up. I know how to work out perpendicular gradients and how to substitute coordinates in to find c, but I don't understand how to use the ratio of the line segment to work out the coordinates of M.
(edited 5 years ago)
Reply 1
Here's the question
can you post the question ?

:holmes:
Original post by Anthos
Here's the question

If you know about ratio theorem, you can use it

You can try a vector approach. Find AB vector

Represent A and B on a diagram

Find AM vector then find position vector of M

Find gradient of AB. Find gradient of perpendicular line to AB.

Find equation using the gradient and coordinates of M
Reply 4
The product of the two gradients make -1. Thus you have a point M and a gradient therefore the line.
Reply 5
Original post by golgiapparatus31
If you know about ratio theorem, you can use it

You can try a vector approach. Find AB vector

Represent A and B on a diagram

Find AM vector then find position vector of M

Find gradient of AB. Find gradient of perpendicular line to AB.

Find equation using the gradient and coordinates of M

I haven't learnt about vectors yet in class, so I'm probably going to have to teach myself this.
Original post by Anthos
I haven't learnt about vectors yet in class, so I'm probably going to have to teach myself this.

You can simplify the ratio 2:4 to 1:2.

You can try finding a general point on line AB.

You can try using distance formula and find coordinates of M
Reply 7
Original post by Anthos
I haven't learnt about vectors yet in class, so I'm probably going to have to teach myself this.

You don't need vectors - you have a formula for the distance between two points - so find the point two sixths of the way towards that point.
I think I got the answer
@Anthos Basically I think this is right but not definitely.

1) I found the gradient of AB and using this I found the gradient of the perpendicular line by doing (-1/gradient)

2) I then multiplied the differences in y and x by (2/6) because that's he ratio of the line from A to M.

3) Using the figures from the previous step I added them to the x any coordinates of A, as you do to give the coordinates of point M

4) Then all I did was put the new coordinates and gradient into the equation y=mx+c to find C (y intercept) and there you go!

Spoiler

Reply 10
Original post by thestudent33
@Anthos Basically I think this is right but not definitely.

1) I found the gradient of AB and using this I found the gradient of the perpendicular line by doing (-1/gradient)

2) I then multiplied the differences in y and x by (2/6) because that's he ratio of the line from A to M.

3) Using the figures from the previous step I added them to the x any coordinates of A, as you do to give the coordinates of point M

4) Then all I did was put the new coordinates and gradient into the equation y=mx+c to find C (y intercept) and there you go!

Spoiler



You got the right answer but I'm still not sure how to do this :frown:
Original post by Anthos
You got the right answer but I'm still not sure how to do this :frown:


PM me and I can giude you through it if you want
Original post by Anthos
You got the right answer but I'm still not sure how to do this :frown:


This should help
Reply 13
Original post by thestudent33
This should help

Thank you so much. That screenshot helped me understand. I did another question like this and got it right.
Original post by Anthos
Thank you so much. That screenshot helped me understand. I did another question like this and got it right.


No problem :smile:

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