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?

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- Aug 6th 2009, 12:22 AMbluffmaster.roy.007any 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?

- Aug 6th 2009, 12:42 AMMush
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. - Aug 6th 2009, 01:21 AMbluffmaster.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 - Aug 6th 2009, 01:39 AMMush
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. - Aug 6th 2009, 05:34 AMmr fantastic