1. ## any general method

In a coordinate system, if three points (5, 3), (x, 3) and (3, 2) lie on a same line, then find a value of x?

2. Originally Posted by bluffmaster.roy.007
In a coordinate system, if three points (5, 3), (x, 3) and (3, 2) lie on a same line, then find a value of x?
It's a straight line, therefore it has an equation of the form:

$\displaystyle y = mx+c$

Where m is the gradient and c is the y-intercept.

To find m, use the following:

$\displaystyle m = \frac{y_2 - y_1}{x_2-x_1}$

Using the coordinates that have no unknowns.

Then find the y intercept by plugging one of the coordinates into your new equation and solve for c.

One you've done that, put the points (x,3) into the equation and solve for x.

3. not able to solve can u show me how to since slope of

the first two cordinates is zero so can the value of x be 5 ....what is the value of x

4. Originally Posted by bluffmaster.roy.007
not able to solve can u show me how to since slope of

the first two cordinates is zero so can the value of x be 5 ....what is the value of x
The slope is not zero. You have two coordinates (5,3) and (3,2).

Therefore, the gradient is calculated as follows:

$\displaystyle m = \frac{3-2}{5-3} = \frac{1}{2}$

So you know that the equation is:

$\displaystyle y = \frac{1}{2}x + C$.

Now you have to find C. Do this by taking one of the coordinates (either (5,3) or (3,2)) and plugging it into the equation, and solve for C.

$\displaystyle 3 = \frac{1}{2} (5) + C$

$\displaystyle \therefore C = 3 - \frac{5}{2} = \frac{1}{2}$

So you're equation is $\displaystyle y = \frac{1}{2}x + \frac{1}{2}$

Now, plug in the coordinate (x,3) and solve for x.

5. Originally Posted by bluffmaster.roy.007
In a coordinate system, if three points (5, 3), (x, 3) and (3, 2) lie on a same line, then find a value of x?
If you plot (5, 3) and (3,2) and run a line through them it is clear that if (x, 3) lies on this line then x = 5.