Question

1. quadrilaterals abcd, abcd and abcd are shown on the coordinate grid.

complete the table by writing the written and algebraic descriptions with the appropriate transformation.

1. 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 identify 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 identify or describe this transformation accurately?

Explanation:

Step1: Analyze the translation rule

For a translation of \(k\) units up, the algebraic rule is \((x,y)\to(x,y + k)\). Here \(k = 2\).

Step2: Apply the rule to each vertex

• For vertex \(A(2,-1)\):

Using the rule \((x,y)\to(x,y + 2)\), we substitute \(x = 2\) and \(y=-1\).
\(A'(2,-1 + 2)=(2,1)\)

• For vertex \(B(-3,0)\):

Substitute \(x=-3\) and \(y = 0\) into \((x,y)\to(x,y + 2)\)
\(B'(-3,0 + 2)=(-3,2)\)

• For vertex \(C(-1,4)\):

Substitute \(x=-1\) and \(y = 4\) into \((x,y)\to(x,y + 2)\)
\(C'(-1,4+ 2)=(-1,6)\)

Answer:

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