Which one of the following does not describe the line through the points (1,2) and (3,4)?
i) (x,y)=(1,2)+t(2,2)
ii) (x,y)=(3,4)+t(2,2)
iii) (x,y)=(1-t)(1,2)+t(3,4)
iv) (x,y)=(1,2)+t(3,4)
v) (x,y)=(1,2)+t(1,1)
How do i solve this?
Thanks!
Which one of the following does not describe the line through the points (1,2) and (3,4)?
i) (x,y)=(1,2)+t(2,2)
ii) (x,y)=(3,4)+t(2,2)
iii) (x,y)=(1-t)(1,2)+t(3,4)
iv) (x,y)=(1,2)+t(3,4)
v) (x,y)=(1,2)+t(1,1)
How do i solve this?
Thanks!
The direction of the line is indicated by the vector (3, 4) - (1, 2) = <2, 2>.
Any point on the line plus a multiple of that vector is a valid representation of the line.
Note that iii) is equivalent to i) after simplifying.
In short, the "wrong" answer is iv), since <3, 4> is not a multiple of <2, 2>.