Question

use your knowledge of reflections to complete parts (a) and (b) below

a. conjecture what the image of a point with coordinates (x,y) will be under the transformation
eflect in the line y = -x\. conjecture what the image of a point with coordinates (x,y) will be under the transformation
eflect in the x - axis.\

b. suppose a point p with coordinates (x,y) is reflected in the line y = -x and then its image is reflected in the x - axis to obtain p. what are the coordinates of p in terms of x and y?

a. the coordinates of the image point from the transformation
eflect in the line y = -x\ are ((-y, -x)).
the coordinates of the image point from the transformation
eflect in the x - axis\ are
(\begin{cases}(-y, -x)\\(x, -y)\\(y, x)\\(-x, y)end{cases})

Explanation:

Step1: Recall the rule for reflection in the x - axis

When a point \((x,y)\) is reflected in the \(x\) - axis, the \(x\) - coordinate remains the same and the \(y\) - coordinate changes its sign.
If the original point is \((x,y)\), after reflection in the \(x\) - axis, the new point is \((x,-y)\)

Answer:

The coordinates of the image point from the transformation "Reflect in the \(x\) - axis" are \((x, - y)\)