Question

1. the coordinates of figure tuvw and its image, tuvw, are given below. t(-4,1), u(-1,-6), v(6,-4), w(2,1) t(-8,1), u(-5,-6), v(2,-4), w(-2,1) name the transformation that takes tuvw to tuvw. be specific

Explanation:

Step1: Analyze the x - coordinates

For point \(T(-4,1)\) and \(T'(-8,1)\), \(x\) - coordinate changes from \(-4\) to \(-8\). For point \(U(-1,-6)\) and \(U'(-5,-6)\), \(x\) - coordinate changes from \(-1\) to \(-5\). For point \(V(6,-4)\) and \(V'(2,-4)\), \(x\) - coordinate changes from \(6\) to \(2\). For point \(W(2,1)\) and \(W'(-2,1)\), \(x\) - coordinate changes from \(2\) to \(-2\).
The rule for the \(x\) - coordinate is \(x\to x - 4\) (e.g., \(-4-4=-8\), \(-1 - 4=-5\), \(6-4 = 2\), \(2-4=-2\)).

Step2: Analyze the y - coordinates

The \(y\) - coordinates of \(T(1)\), \(U(-6)\), \(V(-4)\), \(W(1)\) and their images \(T'(1)\), \(U'(-6)\), \(V'(-4)\), \(W'(1)\) remain the same.

Answer:

A translation \(4\) units to the left.