How to find intersection point of three lines if not graphed? Please Help!!!!?

Question

How to find intersection point of three lines if not graphed? Please Help!!!!?

Answer 1

In 2D world, if two lines are not parallel , there WILL be an intersection point for them , and this point is unique.

But about 3 lines meeting each other , many senarios can be predicted . (a) they maybe parallel , (b) they meet each other in 3 different points , and (c) they meet each other at one point.

So, they only way to calculate , is to find intersection point of each two lines (As we discussed in your previous question) and find out which senario is true for three lines.

for example consider 3 lines as

(a) Y = 2X + 4

(b) Y= 5X - 8

(c) Y= 7X + 3

now , we calculate intersection point of (a) and (b)

You remember that Point i1 was : i(4,12) .

About (a) and (c) , Point i2 can be found in same way as : i2(0.2,4.4)

And for lines (b) and (c) we can calculate int. point as : i3(-5.5,-35.5)

So, for these 3 lines , we have 3 intersection points and we found them by calculating each 2 lines seperatley.

You can apply same method for lines with one intersection point . in that case , you will find a unique set of coordination (x,y) for each 2 lines . like these 3 lines

(a) Y= 2X + 4

(b) Y= 5X - 8

(c) Y= -2X + 32

These 3 lines meet each other at point : i1=i2=i3(4,12)

In summary, you have to calculate intersection point of lines a,b and c as int. point of (a) and (b) , int. point (a) and (c) and int. point (b) and (c). This may gives you 3 different points or only 1 point .

Wish you luck.

Answer 2

Three lines with variables x, y, and z intersect at point (x, y, z) when all the equations of the three lines are true at x, y, and z.

The equations of the three lines must be given; three equations in three unknowns.

You must determine the values of the unknowns x, y, and z one at a time using ANY of the following methods:

By elimination

By substitution

By comparison

By matrices

By graphing (not advisable, since you would have to plot points in  3-dimensional space; difficult to visualize)

Once you've found the x, y, and z values, you need to check whether this set of values makes ALL the equations true. If so, good job!

We may better help you if you provide a set of 3 equations in 3 unknowns that we can work on.

Answer 3

If the 3 lines are parallel, they won't intersect.