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
options:
(y,x)
(x, -y)
(-y, -x)
(-x,y)

Explanation:

Step1: Reflection in the line \(y = -x\)

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

Step2: Reflection in the \(x -\)axis

The rule for reflecting a point \((a,b)\) in the \(x -\)axis is \((a,b)\to(a,-b)\).
Let the image of \(P(x,y)\) after reflection in \(y = -x\) be \(P'( - y,-x)\). Then reflecting \(P'(-y,-x)\) in the \(x -\)axis:
Substitute \(a=-y\) and \(b = -x\) into the \(x -\)axis reflection rule. We get \((-y,-(-x))=(-y,x)\)

Answer:

The coordinates of \(P''\) are \((-y,x)\)