Question

translations: classwork

1. write three different translation rules for which the image of \\( \triangle a b c \\) has a vertex at

the origin. (15 points)

graph the image of each figure under the given translation.(5 points each)

1. \\( t _ { < - 1,4 > } : ( \triangle a b c ) \\)
2. \\( t _ { ( x + 3, y - 3 ) } : ( j k l m ) \\)

1. if \\( t _ { < 10,7 > } : ( q r s t ) = q ^ { prime } r ^ { prime } s ^ { prime } t ^ { prime } \\), what translation maps \\( ^ { prime } q ^ { prime } r ^ { prime } s ^ { prime } t ^ { prime } \\) onto \\( q r s t \\) ? (10point)

1. \\( \triangle x y z \\) has coordinates \\( x ( 2,3 ) , y ( 1,4 ) \\), and \\( z ( 8,9 ) \\). a translation maps \\( x \\) to \\( x ^ { prime } ( 4,8 ) \\).

what are the coordinates for \\( y ^ { prime } \\) and \\( z ^ { prime } \\) for this translation? (10 points)

Explanation:

Step1: Find the translation rule from \(X(2,3)\) to \(X'(4,8)\)

The \(x\) - coordinate changes from \(2\) to \(4\), so \(\Delta x=4 - 2=2\). The \(y\) - coordinate changes from \(3\) to \(8\), so \(\Delta y=8 - 3 = 5\). The translation rule is \(T_{<2,5>}\).

Step2: Apply the translation rule to \(Y(1,4)\)

For the \(x\) - coordinate of \(Y'\): \(x'=1+2 = 3\). For the \(y\) - coordinate of \(Y'\): \(y'=4 + 5=9\). So \(Y'(3,9)\).

Step3: Apply the translation rule to \(Z(8,9)\)

For the \(x\) - coordinate of \(Z'\): \(x'=8+2=10\). For the \(y\) - coordinate of \(Z'\): \(y'=9 + 5=14\). So \(Z'(10,14)\).

Answer:

The coordinates of \(Y'\) are \((3,9)\) and the coordinates of \(Z'\) are \((10,14)\)