The vertices of a rectiſngle are R(-5, -5), S(-1,-5), T(-1, 1), and U(-5,1). A translation maps R to the point (-4, 2). Find the translation rule and the image of U.

The translation rule is T (x, y) → (x + 1, y + 7)

The image of point U is (-4, 8)

Step-by-step explanation:

Let us revise the rule of translation

∵ Point R = (-5, -5)

∵ Point R' = (-4, 2)

∵ -4 > -5 and 2 > -5

→ That means point R translated to the right and up T (x, y) → (x + h, y + k)

∴ h = -4 - (-5) = -4 + 5 = 1 unit

∴ k = 2 - (-5) = 2 + 5 = 7 units

→ By using the 1st and 3rd rules above

∴ The translation rule is T (x, y) → (x + 1, y + 7)

∵ Point U = (-5, 1)

→ By using the rule of translation above

∴ U' = (-5 + 1, 1 + 7)

∴ U' = (-4, 8)

∴ The image of point U is (-4, 8)

v = 1/3 a^2h

step-by-step explanation:

the volume is 1/3 a^2h.