You will need

- The points defined by coordinates.

Instruction

1

If you are given

**the points**with coordinates (x1, Y1, z1), (x2, Y2, z2), (X3, Y3, z3), find the equation of the**straight**, using the coordinates of any two points, for example, first and second. To do this, substitute the appropriate values into the equation**of the straight**: (x-x1)/(x2-x1)=(u-U1)/(U2-U1)=(z-z1)/(z2-z1). If one of the denominators is zero, just Paranaita to zero the numerator.2

Find the equation of the

**straight**, knowing two**points**with coordinates (x1, Y1), (x2, Y2), is even simpler. To do this, substitute values in formula (x-x1)/(x2-x1)=(u-U1)/(U2-U1).3

Having obtained the equation of the

**straight**line that passes through two**points**,, substitute the values of the coordinates of the third**point**into it instead of the variables x and y. If equality happened is correct, then all three**points**lie on the same**straight**. Similarly, you can check the affiliation of this**straight**.4

Check the affiliation of all points

**direct**, checking the equality of the tangents of the angles of the connecting segments. To do this, check whether a true equality (x2-x1)/(X3-x1)=(U2-U1)/(U3-U1)=(z2-z1)/(z3-z1). If one of the denominators is zero, then a single**straight**should satisfy the condition x2-x1=X3-x1, Y2-Y1=Y3-Y1, z2-z1=z3-z1.5

Another way to verify the ownership of the three points

**of direct**– count the area of the triangle which they form. If all**points**lie on**a straight**, then its area will be zero. Substitute the coordinate values into the formula: S=1/2((x1-X3)(Y2-Y3)-(x2-X3)(Y1-Y3)). If after all the calculations you got zero - so the three**points**lie on the same**straight**.6

To find the solution of the problem graphically, draw the coordinate plane and find

**the point**at the specified coordinates. Then draw a line through two of them and continue to the third**point**, let's see if she would pass through it. Note, this method is suitable only for points in the plane with coordinates (x, y), if the point set in space and has coordinates (x, y, z), then this method is not applicable.