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 - coordinate changes

For point T: - 4 to - 8, change is - 8-( - 4)=-4. For point U: - 1 to - 5, change is - 5-( - 1)=-4. For point V: 6 to 2, change is 2 - 6=-4. For point W: 2 to - 2, change is - 2 - 2=-4.

Step2: Analyze y - coordinate changes

For all points T, U, V, W, the y - coordinates remain the same (1 for T and W, - 6 for U, - 4 for V).

Answer:

a translation of 4 units to the left