Question

graph \\( \triangle a b c \\) with vertices \\( a ( - 2,3 ) , b ( 2,2 ) \\), and \\( c ( - 1,0 ) \\) and its image after the glide reflection.
translation: \\( ( x , y ) \
ightarrow ( x - 1 , y ) \\)
reflection: in the \\( x \\)-axis
polygon
undo
redo
\\( x \\) reset

Explanation:

Step1: Apply translation

For a point \((x,y)\), the translation \((x,y)\to(x - 1,y)\)

• For \(A(-2,3)\): \(x=-2,y = 3\), after translation \(x'=-2-1=-3,y'=3\), so \(A'(-3,3)\)
• For \(B(2,2)\): \(x = 2,y=2\), after translation \(x'=2 - 1=1,y'=2\), so \(B'(1,2)\)
• For \(C(-1,0)\): \(x=-1,y = 0\), after translation \(x'=-1-1=-2,y'=0\), so \(C'(-2,0)\)

Step2: Apply reflection in the \(x -\)axis

The rule for reflection in the \(x -\)axis is \((x,y)\to(x,-y)\)

• For \(A'(-3,3)\): after reflection \(A''(-3,-3)\)
• For \(B'(1,2)\): after reflection \(B''(1,-2)\)
• For \(C'(-2,0)\): after reflection \(C''(-2,0)\)

To graph \(\triangle ABC\) and its image:

• Plot the original points \(A(-2,3)\), \(B(2,2)\) and \(C(-1,0)\) and connect them to form \(\triangle ABC\)
• Plot the translated - reflected points \(A''(-3,-3)\), \(B''(1,-2)\) and \(C''(-2,0)\) and connect them to form the image of \(\triangle ABC\) after the glide - reflection.

Answer:

The vertices of the image of \(\triangle ABC\) after the glide - reflection (translation \((x,y)\to(x - 1,y)\) followed by reflection in the \(x -\)axis) are \(A''(-3,-3)\), \(B''(1,-2)\) and \(C''(-2,0)\)