Question

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Question is :
Prove that two distinct lines cannot have more than one point in common .

Answer 1

Lets assume they have more than one point in common.
Let the points be (x1,y1) and (x2,y2)

Slope of 1st line=(y2-y1)/(x2-x1)
Slope of second line will also be same as above because these two points lie on the second line also.

Since slope of line1=slope of line2

These two lines become similar in this case.

So our assumption"two distinct lines have more than one point in common"
is WRONG.

So,two distinct lines cannot have more than one point in common.:-)

Answer 2

Hello Mate

T.p=> Lines line one and line 2 have only one point in common.

Let the Line (1 and 2) intersect at two distinct points say F and H.Then Line one contains points F and H.

and, even line two contains points F and H.

So two line (1 and 2) pass through two distinct points F and H.

(But only one line can pass through two different points.)   (axiom 3)-Euclid

so, the assumption of that two lines can pass through two distinct point is incorrect.

Hence, two lines cannot pass through two distinct points.

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