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# GCSE equation of a line watch

1. P has coordinates (–9, 7)

Q has coordinates (11, 12)

M is the point on the line segment PQ such that PM: MQ = 2: 3

Line L is perpendicular to the line segment PQ.

L passes through M.

Find an equation of L.

Can someone go through this question with me?
2. There are quite a lot of small steps you have to do here. To start with, you have to find the coordinates of M. Is this something you can do? It might help to have the ratio part put into normal English - twice the distance from P to M is three times the distance from M to Q.
3. (Original post by VVDOOMVV)
Find an equation of L.

Can someone go through this question with me?
You need to start by finding the coordinates of M. Start by drawing a diagram showing P, M and Q where PM : MQ = 2 : 3 (you don't need to draw this accurately in your diagram). Label the coordinates of P and Q in your diagram.

Next the important thing to realise is that if PM : MQ = 2 : 3 then the ratio of the horizontal distance from P to M and from M to Q must also be in the ratio 2 : 3. This is due to similar triangles and the same thing can be said for the vertical distance.

So see if you can use this to work out the coordinates of M. Please show us your working and diagram that you've drawn if you get stuck.
4. You can find the gradient for PQ from the co-ordinates. The gradient of L is then, the negative reciprocal of PQ. M can be found and then substituting into equation for L, you can find the full equation for L

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Updated: January 9, 2017
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