In a coordinate system, if three points (5, 3), (x, 4) and (3, 2) lie on a same line, then find a value of x?
Now, the slope appears to be 1/2 from the two given points.
Does this mean that x will be a number than when used to calculate the slope of the line with any of the other two points will still be 1/2? In this case, 7? Or, do we have to develop the equation of the line and substitute (x,4) into the equation of the line in which case I get 5.
They should both give you the same answer. Can you show a bit more work?
You should get the same answer from both methods, because they are somewhat related. The formula I use for finding the gradient is:
Then, I would use:
To get the equation of the line. But, since both equals to m, I can directly say that:
So, it's the same as making both gradients equal.
A shorter way that I came to.
Rearrange your coordinates so that the y coordinates are in ascending order.
(3, 2) , (5, 3) , (x , 4)
Looking at the y coordinates, it increases by 1 each time. And since all the points lie on a straight line, you can conclude that (5, 3) is the midpoint of (3, 2) and (x, 4). In which case, you will have an arithmetic sequence for the x coordinate too. It's 3, 5 then x. Since it increases by 2, you add 2 to 5 to give 7, the value of x.
In any case, you should get x = 7.
Wow nevermind. Simple arithmetic kills :-p