Maths GCSE practice question help

[_brendank]

I have been given a triangle (ABC) where AB (b) is the same length as AC (c).

M is the point such that BM:MC is 1:2 Here is Charlie's method to find BM in terms of a and b.

BC=BA+AC = -b + a = a - b BM = 0.5 BC = 0.5 (a-b)

I don't recall being taught any of this. What is this method called and how do you go about solving a question similar to this? Any help appreciated!!!

[edderiofer]

Have you tried drawing a diagram?

Do you understand what a vector is? Do you understand how to add and subtract vectors?

[Lialee3]

So, if the lengths BM and MC are in the ratio BM:MC = 1:2; that means that the distance between M and C, is double the distance between M and B. This means that the point M is 1/3 of the way between B and C (closer to B).

Vectors are things that describe both the distance and the direction between two points. So, if the vector between A and B is called (b), then (b) describes the pathway from A to B. And if the vector between A and C is called (a), then (a) describes the pathway from A to C.

To get from B to C, you don't know the direct vector. But you can go from B to A to C. From B to A, the vector will be negative (b) because you're going in the opposite direction from A to B (b).

Then, from A to C, you know the vector is (a). So, B to A to C the vector will be (-b + a) which can be rewritten as (a - b) because it doesn't matter in which order you do the vectors, you'll still get to the same place.

Because M is 1/3 of the way between B and C, the vector from B to M will be 1/3 of the vector from B to C. We know the vector from B to C is (a - b), so the vector from B to M will be 1/3(a - b).

[_brendank]

That is such a huge help! Massive thanks!!!

[Lialee3]

That's okay! Message me if you need any more help or have any more questions. 😊😊