Find the image of P(5,-3)under each of the given transformations:
1. r x-axis(5,-3)?
2. Rorigin (-5,3)?
3. R90 (3,5)?
4.T 0,3 (5,0)?
5.r x-axis o T2,2 (7,1)?
6. r x-axis o r y=x (-3,-5)?
7. r y=x o r x-axis (3,5)?
8. R(2,2) o T5,-3 (12,-4)?
Thank you!
To find the image of a point under a given transformation, we need to apply the transformation to the coordinates of the point.
1. r x-axis reflects the point across the x-axis.
For point P(5, -3), the image under r x-axis will have the same x-coordinate but the opposite sign for the y-coordinate. So the image is P(5, 3).
2. Rorigin rotates the point 180 degrees about the origin.
For point P(-5, 3), the image under Rorigin will have the opposite signs for both x and y coordinates. So the image is P(5, -3).
3. R90 rotates the point 90 degrees clockwise about the origin.
For point P(3, 5), the image under R90 will have the coordinates (-y, x). So the image is P(-5, 3).
4. T 0,3 translates the point 0 units horizontally and 3 units vertically.
For point P(5, 0), the image under T 0,3 will have the same x-coordinate but the y-coordinate will increase by 3. So the image is P(5, 3).
5. r x-axis o T2,2 applies two transformations sequentially: reflection across the x-axis and then translation 2 units horizontally and 2 units vertically.
For point P(7, 1), first, we reflect across the x-axis to get (7, -1) and then translate 2 units horizontally and 2 units vertically to get (9, 1). So the image is P(9, 1).
6. r x-axis o r y=x applies two transformations sequentially: reflection across the x-axis and then reflection across the line y = x.
For point P(-3, -5), first, we reflect across the x-axis to get (-3, 5) and then reflect across the line y = x to get (5, -3). So the image is P(5, -3).
7. r y=x o r x-axis applies two transformations sequentially: reflection across the line y = x and then reflection across the x-axis.
For point P(3, 5), first, we reflect across the line y = x to get (5, 3) and then reflect across the x-axis to get (5, -3). So the image is P(5, -3).
8. R(2,2) o T5,-3 applies two transformations sequentially: rotation 90 degrees clockwise about point (2, 2), and then translation 5 units horizontally and -3 units vertically.
For point P(12, -4), first, we rotate 90 degrees clockwise about (2, 2) to get (0, 14), and then translate 5 units horizontally and -3 units vertically to get (5, 11). So the image is P(5, 11).
Remember to check your calculations and verify the transformations to get accurate results.