Question

1. write an algebraic representation for the reflection.

(x,y)→x,−y)

b the table represents the location of qrst before and after a reflection. use the table to answer 3-5.

pre-image	image
r(-9, -2)	r(9, -2)
s(-4, -2)	s(4, -2)
t(-4, -8)	4 ?-8

1. give a verbal description of the transformation.
2. which best represents the transformation algebraically?

a. (x, -y) b. (-x, y) c. (-x, -y) d. (x + 18, y)

1. find the location of t.

c use the graph to mark each statement as true or false. correct any false statements.

____ 6. the pre-image is in quadrant iii.
____ 7. the orientation of the vertices changed.
____ 8. the reflection can be represented by (-x, y).
____ 9. the line of reflection is the x-axis.
____ 10. the pre-image and image are congruent.

Explanation:

Step1: Analyze the transformation of coordinates

Looking at the pre - image and image coordinates (e.g., \(Q(-9,-8)\) to \(Q'(9,-8)\), \(R(-9,-2)\) to \(R'(9,-2)\), \(S(-4,-2)\) to \(S'(4,-2)\)), we can see that the \(x\) - coordinate changes sign while the \(y\) - coordinate remains the same.

Step2: Determine the algebraic representation

For a point \((x,y)\) in the pre - image, the image point is \((-x,y)\) (since \(x\) becomes \(-x\) and \(y\) stays the same). Let's check the options:

• Option a: \((x,-y)\) changes the sign of \(y\), not \(x\), so it's incorrect.
• Option b: \((-x,y)\) changes the sign of \(x\) and keeps \(y\) the same, which matches our observation.
• Option c: \((-x,-y)\) changes the sign of both \(x\) and \(y\), which is incorrect.
• Option d: \((x + 18,y)\) is a translation, not a reflection, so it's incorrect.

Step3: Find the location of \(T'\)

The pre - image of \(T\) is \(T(-4,-8)\). Using the transformation \((x,y)\to(-x,y)\), we substitute \(x=-4\) and \(y = - 8\) into the transformation. So \(x\) becomes \(-(-4)=4\) and \(y\) remains \(-8\). So \(T'\) is \((4,-8)\).

Answer:

1. B. \((-x,y)\)
2. \((4,-8)\)