Question

1. translate the $\triangle abc$ 4 units to the right and 6 units up.

draw the image $\triangle abc.
this translation can be written as: $(x, y) \to (x\underline{quad}, y\underline{quad}).
what are the coordinates of?
$a(-2, -2) \to a\underline{quad}$
$b(1, -5) \to b\underline{quad}$
$c(-5, -5) \to c\underline{quad}$

Explanation:

Step1: Define translation rule

Right adds 4 to $x$, up adds 6 to $y$:
$(x, y) \to (x + 4, y + 6)$

Step2: Calculate $A'$ coordinates

Substitute $A(-2, -2)$:
$A' = (-2 + 4, -2 + 6) = (2, 4)$

Step3: Calculate $B'$ coordinates

Substitute $B(1, -5)$:
$B' = (1 + 4, -5 + 6) = (5, 1)$

Step4: Calculate $C'$ coordinates

Substitute $C(-5, -5)$:
$C' = (-5 + 4, -5 + 6) = (-1, 1)$

Answer:

Translation rule: $(x, y) \to (x + 4, y + 6)$
$A' = (2, 4)$
$B' = (5, 1)$
$C' = (-1, 1)$