Question

in exercise 6, graph △jkl with vertices j(2, 3), k(-2, 1), l(-1, 5) and its image after the glide reflection. draw all 3 triangles. use a ruler!

1. translation: (x, y) → (x - 1, y + 2)

reflection: in the x - axis

Explanation:

Step1: Calculate translated vertices

For vertex \(J(2,3)\):
Using the translation \((x,y)\to(x - 1,y + 2)\), we have \(x=2-1 = 1\) and \(y=3 + 2=5\). So \(J'(1,5)\)
For vertex \(K(-2,1)\):
\(x=-2-1=-3\) and \(y=1 + 2=3\). So \(K'(-3,3)\)
For vertex \(L(-1,5)\):
\(x=-1-1=-2\) and \(y=5 + 2=7\). So \(L'(-2,7)\)

Step2: Calculate reflected vertices (after translation)

The rule for reflection in the \(x -\)axis is \((x,y)\to(x,-y)\)
For \(J'(1,5)\), the reflected vertex \(J''(1,-5)\)
For \(K'(-3,3)\), the reflected vertex \(K''(-3,-3)\)
For \(L'(-2,7)\), the reflected vertex \(L''(-2,-7)\)

Step3: Graph the triangles

• Graph \(\triangle JKL\) with vertices \(J(2,3)\), \(K(-2,1)\), \(L(-1,5)\)
• Graph the translated triangle \(\triangle J'K'L'\) with vertices \(J'(1,5)\), \(K'(-3,3)\), \(L'(-2,7)\)
• Graph the glide - reflected triangle \(\triangle J''K''L''\) with vertices \(J''(1,-5)\), \(K''(-3,-3)\), \(L''(-2,-7)\) using a ruler to connect the vertices properly.

Answer:

Follow the above three - step process to graph the three triangles \(\triangle JKL\), \(\triangle J'K'L'\) (translated), and \(\triangle J''K''L''\) (glide - reflected) on the coordinate plane.