Question

rectangle ( abcd ) has vertices at ( (1,8),(6,8),(6,5) ), and ( (1,5) ). rectangle ( a^{prime} b^{prime} c^{prime} d^{prime} ) is the image formed when rectangle ( abcd ) is reflected across the ( y )-axis and then translated 4 units down.
plot rectangle ( a^{prime} b^{prime} c^{prime} d^{prime} ) on the grid.

Explanation:

The problem describes reflecting a rectangle across the y - axis and then translating it down. This involves coordinate transformations.

Step1: Reflect across the y - axis

The rule for reflecting a point \((x,y)\) across the y - axis is \((-x,y)\).
For point \(A(1,8)\), after reflection, \(A'(-1,8)\).
For point \(B(6,8)\), after reflection, \(B'(-6,8)\).
For point \(C(6,5)\), after reflection, \(C'(-6,5)\).
For point \(D(1,5)\), after reflection, \(D'(-1,5)\).

Step2: Translate 4 units down

The rule for translating a point \((x,y)\) 4 units down is \((x,y - 4)\).
For \(A'(-1,8)\), after translation, \(A''(-1,8 - 4)=(-1,4)\).
For \(B'(-6,8)\), after translation, \(B''(-6,8 - 4)=(-6,4)\).
For \(C'(-6,5)\), after translation, \(C''(-6,5 - 4)=(-6,1)\).
For \(D'(-1,5)\), after translation, \(D''(-1,5 - 4)=(-1,1)\).

Answer:

Plot the points \(A''(-1,4)\), \(B''(-6,4)\), \(C''(-6,1)\), and \(D''(-1,1)\) on the grid and connect them to form rectangle \(A'B'C'D'\).