Find the Coordinates

[Guest]

What are the coordinates of the point that is the image of Z(4, -1) after a reflection in the point (0, 3)?

MY WORK:

I think the question is asking for z'(-a, b).

So, I plugged the values given for point Z into z'(-a,b) and got z'(-4, 1) but the book's answer is (-4, 7).

Who is right? What did I do wrong?

 

[tkhunny]

What are the coordinates of the point that is the image of Z(4, -1) after a reflection in the point (0, 3)?

Quick Reality Check

0-4 = -4 ==> 0+(-4) = -4
3-(-1) = 4 ==> 3+4 = 7

Notice how -1 and 1 are on the same side of 3. That can't be a reflection through a point.

 

[Guest]

ok

You subtracted? The chapter does not explain to do that at all. I now know what to do.

 

[pka]

The mapping is <4t,-4t+3>!
When t=1 we get (4,-1).
When t=-1, we get the reflection through (0,3) or (-4,7).

 

[Guest]

ok

I totally got it.

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