Question

1. reflect bcde about the x - axis and then translate bcde 5 units left. find the indicated coordinates. b ( , ) c ( , ) d ( , ) e ( , )

Explanation:

Step1: Find the coordinates of \(B\), \(C\), \(D\), \(E\)

Assume each grid is \(1\) unit. From the graph, \(B(9,1)\), \(C(5,1)\), \(D(3,5)\), \(E(7,5)\)

Step2: Reflect over the \(x -\)axis

The rule for reflecting a point \((x,y)\) over the \(x -\)axis is \((x,-y)\).
For \(B(9,1)\), after reflection \(B'(9, - 1)\)
For \(C(5,1)\), after reflection \(C'(5, - 1)\)
For \(D(3,5)\), after reflection \(D'(3,-5)\)
For \(E(7,5)\), after reflection \(E'(7,-5)\)

Step3: Translate 5 units left

The rule for translating a point \((x,y)\) \(5\) units left is \((x - 5,y)\)
For \(B'(9,-1)\), \(B''=(9 - 5,-1)=(4,-1)\)
For \(C'(5,-1)\), \(C''=(5 - 5,-1)=(0,-1)\)
For \(D'(3,-5)\), \(D''=(3 - 5,-5)=(-2,-5)\)
For \(E'(7,-5)\), \(E''=(7 - 5,-5)=(2,-5)\)

Answer:

\(B''(4,-1)\), \(C''(0,-1)\), \(D''(-2,-5)\), \(E''(2,-5)\)