Question

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) which single transformation will map figure tuvw onto figure tuvw? a translation of 4 units up a translation of 4 units down a translation of 4 units to the left a translation of 4 units to the right

Explanation:

Step1: Analyze x - coordinates change

For point $T$, $x$-coordinate changes from $- 4$ to $-8$ ($-8-(-4)=-4$). For point $U$, $x$-coordinate changes from $-1$ to $-5$ ($-5 - (-1)=-4$). For point $V$, $x$-coordinate changes from $6$ to $2$ ($2 - 6=-4$). For point $W$, $x$-coordinate changes from $2$ to $-2$ ($-2 - 2=-4$). The $y$-coordinates remain the same for all points.

Step2: Determine the transformation

A change in the $x$-coordinate by a negative value while the $y$-coordinate remains constant represents a left - ward translation. Since the change in the $x$-coordinate for all points is $-4$, it is a translation of 4 units to the left.

Answer:

a translation of 4 units to the left