Question

problem 6
point ((x, y)) is reflected over the (y)-axis, and then translated 5 units to the right and 2 units down.
write the generalized coordinates of the image.

Explanation:

Step1: Reflect over y - axis

When a point \((x,y)\) is reflected over the \(y\) - axis, the \(x\) - coordinate changes its sign and the \(y\) - coordinate remains the same. So the coordinates after reflection are \((-x,y)\).

Step2: Translate 5 units right and 2 units down

To translate a point \((a,b)\) \(h\) units to the right, we add \(h\) to the \(x\) - coordinate, and to translate it \(k\) units down, we subtract \(k\) from the \(y\) - coordinate. Here, \(h = 5\) and \(k=2\), and the point after reflection is \((-x,y)\). So the new \(x\) - coordinate is \(-x + 5\) and the new \(y\) - coordinate is \(y-2\).

Answer:

\((-x + 5,y - 2)\)