Question

1. quadrilaterals abcd, abcd and abcd are shown on the coordinate grid
2. triangle lmn has l at (1, -1) and m at (2, 3). triangle lmn has l at (-1, -1) and m is at (3, -2). describe the transformation.

reflection prompt: what helped you identity or describe this transformation accurately?

1. triangle abc has vertices a(2, -1), b(-3, 0), and c(-1, 4). find the vertices of the image of triangle abc after a translation of 2 units up.

reflection prompt: what helped you identity or describe this transformation accurately?

Explanation:

Step1: Understand the translation rule

A translation of 2 units up means that for each vertex \((x,y)\) of the triangle \(ABC\), the \(y -\)coordinate is increased by 2 while the \(x -\)coordinate remains the same. The translation rule is \((x,y)\to(x,y + 2)\).

Step2: Apply the rule to vertex \(A\)

For vertex \(A(2,-1)\), using the rule \((x,y)\to(x,y + 2)\), we substitute \(x = 2\) and \(y=-1\). Then \(y+2=-1 + 2=1\). So \(A'\) has coordinates \((2,1)\).

Step3: Apply the rule to vertex \(B\)

For vertex \(B(-3,0)\), substitute \(x=-3\) and \(y = 0\) into the rule \((x,y)\to(x,y + 2)\). Then \(y + 2=0+2 = 2\). So \(B'\) has coordinates \((-3,2)\).

Step4: Apply the rule to vertex \(C\)

For vertex \(C(-1,4)\), substitute \(x=-1\) and \(y = 4\) into the rule \((x,y)\to(x,y + 2)\). Then \(y+2=4 + 2=6\). So \(C'\) has coordinates \((-1,6)\).

Answer:

The vertices of the image of triangle \(ABC\) after the translation are \(A'(2,1)\), \(B'(-3,2)\) and \(C'(-1,6)\)