Math Is Fun Forum

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Another matrices question

I get the right answer, I'm just wondering if there's a better way of doing it.

"The point (x,y) is transformed to the point (x',y') by means of the transformation

. Find the image of the line y=2x under this transformation."

My method was to rewrite as:

I then said that the gradient is being stretched by 4/3, and the line is then being shifted up by 1, giving y' = 8/3x' + 1. I found the x-intercept to be -3/8, so the shift to the right by 1 then takes the x intercept to 5/8, giving y' = 8/3x' + c. Substituting x' = 5/8, y' = 0 gives c = -5/3, and so the final equation of the transformed line is y' = 8/3x' - 5/3 ⇒ 3y' = 8x' - 5 (which is the answer in the back of the book).

Is there a better way of doing it?

Thanks.

Last edited by Daniel123 (2008-10-12 03:40:38)

Kurre

Member

Registered: 2006-07-18

Posts: 280

Re: Another matrices question

any point on the line has the form (x,2x), so I would just substitute y with 2x in the above equation giving:

x'=3x+1
y'=8x+1

substituting x with (x'-1)/3 gives
y'=8(x'-1)/3+1=8x'/3-5/3

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Another matrices question

Ahh that's better, thanks