A triangle has points A(1, 2), B(1, 6), and C(3, 6) and is reflected over the x-axis and then over the line y = x. A"B"C" are the coordinates of the reflected image. What is the A" coordinate?
reflect over y=0: (x,y) -> (x,-y)
A(1,2) -> A'(1,-2)
B(1,6) -> B'(1,-6)
C(3,6) -> C'(3,-6)
reflect in y=x: (x,y) -> (y,x)
A'(1,-2) -> A*(-2,1)
B'(1,-6) -> B*(-6,1)
C'(3,-6) -> C*(-6,3)
combined image: (x,y) -> (-y,x)
Yes the answer above is correct.
(-6,3)
correct answer
To find the coordinates of the reflected image A", we need to perform two transformations: reflection over the x-axis and reflection over the line y = x.
Step 1: Reflection over the x-axis.
To reflect a point (x, y) over the x-axis, we keep the x-coordinate the same and change the sign of the y-coordinate. In this case, since A(1, 2) lies above the x-axis, its reflection over the x-axis, A', will have the same x-coordinate but a negative y-coordinate (1, -2).
Step 2: Reflection over the line y = x.
To reflect a point (x, y) over the line y = x, we swap the x and y coordinates. Since A'(1, -2) lies on the line y = x, its reflection A" will have the swapped coordinates (-2, 1).
Therefore, the coordinates of the reflected image A" are (-2, 1).