Prisilla performs a series of transformations on a figure in the plane. First she dilates it by a factor of 3 and translates it 5 units to the right. Next she reflects it over the x axis, then over the y axis. Finally she reflects it over the line y=x, translate it 5 units to the left, and dilates it by a factor of 1/3.
The point A (4,3) is on the figure. Perform each of the transformations.
Here's what I got
Dilation: (12,9)
Translation: (17,19)
Reflection over x axis: (17,-9)
Reflection over y axis: (-17,-9)
y=x: (9,-17)
Translation: (4,-22)
Dilation: (1,-7.3)
is it right?
To perform each of the transformations on the point A (4,3) as described:
1. Dilation by a factor of 3:
Multiply each coordinate of A by the dilation factor.
So, (4,3) x 3 = (12, 9)
2. Translation 5 units to the right:
Add 5 to the x-coordinate of A.
So, (12,9) + (5,0) = (17,9)
3. Reflection over the x-axis:
Negate the y-coordinate of A.
So, (17,9) -> (17,-9)
4. Reflection over the y-axis:
Negate the x-coordinate of A.
So, (17,-9) -> (-17,-9)
5. Reflection over the line y=x:
Swap the x and y coordinates of A.
So, (-17,-9) -> (-9,-17)
6. Translation 5 units to the left:
Subtract 5 from the x-coordinate of A.
So, (-9,-17) - (5,0) = (-14,-17)
7. Dilation by a factor of 1/3:
Multiply each coordinate of A by the dilation factor.
So, (-14,-17) x 1/3 = (-(14/3), -(17/3)) ≈ (-4.67,-5.67)
Therefore, the final transformed point after performing all the given transformations on A (4,3) is approximately (-4.67,-5.67).