Question

A point A(-5, -3) is translated by the vector v=⟨2,6⟩ and then reflected about the line x=0. Find the coordinates of A' after the translation and A'' after the reflection.

a) A'(-3, 3), A''(3, 3)
b) A'(3, 3), A''(3, -3)
c) A'(-3, -3), A''(3, -3)
d) A'(3, -3), A''(-3, 3)

Answer 1

Point A' after translation by the vector v=\u27E82,6\u27E9 is A'(-3, 3), and after reflection about the line x=0, the coordinates of A'' are A''(3, 3). The correct answer is option a) A'(-3, 3), A''(3, 3).

Step-by-step explanation:

The process to find the coordinates of A' after the translation and A'' after the reflection starts with translating point A(-5, -3) by the vector v=\u27E82,6\u27E9. Translation means adding the vector components to the original coordinates. After translation, point A' will have coordinates A'(-5+2, -3+6) which simplifies to A'(-3, 3). The next step is reflecting A' about the line x=0. Reflection over x=0 switches the sign of the x-coordinate but keeps the y-coordinate unchanged. Therefore, point A'' will have coordinates A''(3, 3).

The correct answer is a) A'(-3, 3), A''(3, 3).