Question

1. △mpq: m(-4,3), p(-5,8), q(-1,6)

translation: along (-4,-4)
reflection: in y = x

Explanation:

Step1: Translation of points

For a point \((x,y)\) translated along \((a,b)\), the new point is \((x + a,y + b)\).
For \(M(-4,3)\): \(x=-4,a = - 4,y = 3,b=-4\), new \(x=-4-4=-8\), new \(y=3-4=-1\), so \(M'(-8,-1)\)
For \(P(-5,8)\): \(x=-5,a=-4,y = 8,b=-4\), new \(x=-5-4=-9\), new \(y=8 - 4=4\), so \(P'(-9,4)\)
For \(Q(-1,6)\): \(x=-1,a=-4,y = 6,b=-4\), new \(x=-1-4=-5\), new \(y=6-4=2\), so \(Q'(-5,2)\)

Step2: Reflection of translated points in \(y = x\)

For a point \((x,y)\) reflected in \(y=x\), the new point is \((y,x)\)
For \(M'(-8,-1)\): new point \(M''(-1,-8)\)
For \(P'(-9,4)\): new point \(P''(4,-9)\)
For \(Q'(-5,2)\): new point \(Q''(2,-5)\)

Answer:

The new coordinates of the triangle after translation and reflection are \(M''(-1,-8)\), \(P''(4,-9)\), \(Q''(2,-5)\)