Help with GCSE question

I need help with this question:

The points L, M, and N are such that LMN is a straight line.

The coordinates of L are (-3, 1)

The coordinates of M are (4, 9)

Given that LM: MN = 2:3

Find the coordinates of N.

The mark scheme doesn't explain this very well, I thought you could find the difference between the two coordinates, eg (4 - - 3 = 7, 8 - 1 = 8), so (7,8), then could you divide this by 2 and times by 3? So you would get (10.5, 12), then add this to (4,9)?
So I get (14.5, 21), is this right?

Reply 1

mqb2766

21

Original post by Bladerun2

I need help with this question:

The points L, M, and N are such that LMN is a straight line.

The coordinates of L are (-3, 1)

The coordinates of M are (4, 9)

Given that LM: MN = 2:3

Find the coordinates of N.

The mark scheme doesn't explain this very well, I thought you could find the difference between the two coordinates, eg (4 - - 3 = 7, 8 - 1 = 8), so (7,8), then could you divide this by 2 and times by 3? So you would get (10.5, 12), then add this to (4,9)?
So I get (14.5, 21), is this right?

Sounds good, the 2:3 ratio applies to both the x and y coordinates as youve done. Think about a couple of similar triangles if necessary.

(edited 3 months ago)

Reply 2

tonyiptony

11

Well, the answer is right, but do double check you know how this method works. Like for instance, why "divide by 2 and times 3", and why "add this to (4,9)"?

Sidenote: your method makes more sense if you've learned some basic concepts about vectors.

Alternatively, you can use the general formula for this. To find x-coordinate of M (the "middle point"), we have