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 ((x,-y))

b. the coordinates of (p) in terms of (x) and (y) are (square)
options:
((y,-x))
((-y,-x))
((-y,x))
((x,-x))

Explanation:

Step1: Find the image after reflection in \(y = -x\)

When a point \((x,y)\) is reflected in the line \(y=-x\), the rule is \((x,y)\to(-y, -x)\).

Step2: Reflect the new - point in the \(x\) - axis

The rule for reflection in the \(x\) - axis is \((a,b)\to(a, -b)\). If the point after reflection in \(y = -x\) is \((-y,-x)\), then after reflection in the \(x\) - axis, we change the sign of the \(y\) - coordinate. So \((-y,-x)\to(-y,x)\)

Answer:

\((-y,x)\)