If points (1,2)(-1,x)and (2,3) are collinear then value of x is?

Question

Answer

Answer

0

Answer

answer will be 0because if you use method of area of triangle you will get the answeras all points are collinear area of triangle=0then put 0=1/2[1(x-3)-1(3-2)+2(2-x)]you will get0=x-3-3+2+4-2x0=-6+6-xx=0I hope this will help you

Answer

Collinear Points

Collinear points are points that lie on the same line. In other words, if three points are collinear, then the slope of the line passing through any pair of these points will be the same.

Given Points

The given points are (1,2), (-1,x), and (2,3). We need to determine the value of x if these points are collinear.

Find the Slope of the Line

To check if the given points are collinear, we can find the slope of the line passing through any two of these points. Let's calculate the slope of the line passing through the points (1,2) and (-1,x).

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

slope = (y2 - y1) / (x2 - x1)

In this case, the coordinates of the two points are (1,2) and (-1,x). Substituting these values into the formula, we get:

slope = (x - 2) / (-1 - 1)
slope = (x - 2) / -2

Determine the Slope of the Line Passing Through the Third Point

Now, let's find the slope of the line passing through the points (1,2) and (2,3). Using the same formula, we have:

slope = (3 - 2) / (2 - 1)
slope = 1 / 1
slope = 1

Compare the Slopes

Since the three points are collinear, the slopes of the lines passing through any pair of these points should be the same. Therefore, we can equate the two slopes we calculated:

(x - 2) / -2 = 1

Solve for x

To find the value of x, we can cross-multiply and solve for x:

-2 = x - 2
x = 2 - 2
x = 0

Conclusion

Therefore, if the points (1,2), (-1,x), and (2,3) are collinear, then the value of x is 0.

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