Triangle ABC is given by the points A(1,1), B(3,2), C(2,3). Consider each rule of transformation. Does the rule result in an image with points A'(2,2), B'(6,3), and C'(4,4).
(x,y) transforms into (x,y+1) y/n
(x,y) transforms into (2x,2y) y/n
(x,y) transforms into (2x,y+1) y/n
To determine whether each rule of transformation results in an image with the given points A'(2,2), B'(6,3), and C'(4,4), we need to apply each rule to the given triangle and check if the resulting coordinates match the given points.
Let's go through each rule:
1. (x,y) transforms into (x,y+1)
To apply this transformation to each point of the triangle ABC:
A(1,1) -> A'(1,2)
B(3,2) -> B'(3,3)
C(2,3) -> C'(2,4)
The resulting image points do not match A'(2,2), B'(6,3), and C'(4,4). So, the rule (x,y) transforms into (x,y+1) does not result in the given image points.
2. (x,y) transforms into (2x,2y)
To apply this transformation to each point of the triangle ABC:
A(1,1) -> A'(2,2)
B(3,2) -> B'(6,4)
C(2,3) -> C'(4,6)
Again, the resulting image points do not match A'(2,2), B'(6,3), and C'(4,4). Therefore, the rule (x,y) transforms into (2x,2y) also does not yield the given image points.
3. (x,y) transforms into (2x,y+1)
To apply this transformation to each point of the triangle ABC:
A(1,1) -> A'(2,2)
B(3,2) -> B'(6,3)
C(2,3) -> C'(4,4)
Finally, the resulting image points match A'(2,2), B'(6,3), and C'(4,4). Therefore, the rule (x,y) transforms into (2x,y+1) does result in the given image points.
So, the answers are:
1. (x,y) transforms into (x,y+1): No
2. (x,y) transforms into (2x,2y): No
3. (x,y) transforms into (2x,y+1): Yes
just take each point and see whether the rule transforms it to the desired point. For example,
(x,y+1) transforms (2,4) -> (2,5)
Then see which rule takes all 3 points where you want them.