Question

What is the image point of left bracket, 1, comma, minus, 9, right bracket(1,−9) after the transformation T, start subscript, 2, comma, 3, end subscript, circle, r, start subscript, x-axis, end subscriptT 2,3 ​ ∘r x-axis ​ ?

Answer 1

The image point of (1,−9) after the transformation T2,3 ∘ rx-axis is (3, 12), found by first reflecting the point across the x-axis and then translating it right by 2 units and up by 3 units.

Step-by-step explanation:

The student has asked what the image point of (1,−9) would be after applying the transformation T2,3 ∘ rx-axis. To find the transformed point, we must apply the given transformations step by step.

1. Reflection rx-axis: Reflect the point across the x-axis. The x-coordinate remains the same, but the y-coordinate changes sign. Therefore, (1,-9) becomes (1,9).
2. Translation T2,3: Move the reflected point by 2 units right and 3 units up. Thus, (1,9) becomes (1+2, 9+3) which is (3, 12).

The image point after the transformation T2,3 ∘ rx-axis is (3, 12).