Question

the reflection of trapezoid abcd over the y - axis is shown.

1. reflect trapezoid abcd over each given line of reflection. graph and label each image on the coordinate plane and record each images coordinates in the table.

a. reflect trapezoid abcd over the y - axis to form trapezoid abcd.
b. reflect trapezoid abcd over the x - axis to form trapezoid abcd.
coordinates of trapezoid abcd
coordinates of trapezoid abcd
coordinates of trapezoid abcd
a(3,9)
b(3,4)
c(11,4)
d(11,10)
point on trapezoid abcd(x,y)

Explanation:

Step1: Reflection over y - axis

The rule for reflection over the y - axis is \((x,y)\to(-x,y)\).
For point \(A(3,9)\), \(A'\) is \((- 3,9)\).
For point \(B(3,4)\), \(B'\) is \((-3,4)\).
For point \(C(11,4)\), \(C'\) is \((-11,4)\).
For point \(D(11,10)\), \(D'\) is \((-11,10)\).

Step2: Reflection over x - axis

The rule for reflection over the x - axis is \((x,y)\to(x,-y)\).
For point \(A(3,9)\), \(A''\) is \((3,-9)\).
For point \(B(3,4)\), \(B''\) is \((3,-4)\).
For point \(C(11,4)\), \(C''\) is \((11,-4)\).
For point \(D(11,10)\), \(D''\) is \((11,-10)\).

Answer:

Coordinates of Trapezoid \(ABCD\)	Coordinates of Trapezoid \(A'B'C'D'\)	Coordinates of Trapezoid \(A''B''C''D''\)
\(B(3,4)\)	\(B'(-3,4)\)	\(B''(3,-4)\)
\(C(11,4)\)	\(C'(-11,4)\)	\(C''(11,-4)\)
\(D(11,10)\)	\(D'(-11,10)\)	\(D''(11,-10)\)