Question

parallelogram rstu is reflected over the x-axis to produce rstu. write the coordinates of each vertex in the image. r(box, box) s(box, box) t(box, box) u(box, box)

Explanation:

Step1: Find original coordinates

First, identify the coordinates of the original vertices from the graph:

• \( R(-3, -1) \)
• \( S(4, -1) \)
• \( T(2, -5) \)
• \( U(-5, -5) \)

Step2: Apply reflection over x - axis

The rule for reflecting a point \((x, y)\) over the \( x \) - axis is \((x, -y)\).

• For \( R(-3, -1) \):

Using the reflection rule, \( x=-3\), \( y = - 1\), so \( R'(-3,-(-1))=R'(-3,1) \)

• For \( S(4, -1) \):

Using the reflection rule, \( x = 4\), \( y=-1\), so \( S'(4,-(-1))=S'(4,1) \)

• For \( T(2, -5) \):

Using the reflection rule, \( x = 2\), \( y=-5\), so \( T'(2,-(-5))=T'(2,5) \)

• For \( U(-5, -5) \):

Using the reflection rule, \( x=-5\), \( y = - 5\), so \( U'(-5,-(-5))=U'(-5,5) \)

Answer:

\( R'(-3, 1) \)
\( S'(4, 1) \)
\( T'(2, 5) \)
\( U'(-5, 5) \)