Question

the table shows the coordinates of the vertices of $\triangle abc$ and its image.\
\

$\triangle abc$	$\triangle abc$	\
---	---	\
$a(-4, 3)$	$a(-1, 3)$	\
$b(0, 4)$	$b(3, 4)$	\
$c(-3, 1)$	$c(0, 1)$	\

\
which translation maps $\triangle abc$ onto its image?\

• 3 units down\
• 3 units up\
• 3 units to the right\
• 3 units to the left

Explanation:

Step1: Analyze the x - coordinates of point A

For point \(A(-4,3)\) and its image \(A'(-1,3)\), the change in the x - coordinate is \(- 1-(-4)=-1 + 4=3\). The y - coordinate remains the same (\(3 - 3=0\)).

Step2: Analyze the x - coordinates of point B

For point \(B(0,4)\) and its image \(B'(3,4)\), the change in the x - coordinate is \(3 - 0 = 3\). The y - coordinate remains the same (\(4 - 4=0\)).

Step3: Analyze the x - coordinates of point C

For point \(C(-3,1)\) and its image \(C'(0,1)\), the change in the x - coordinate is \(0-(-3)=0 + 3=3\). The y - coordinate remains the same (\(1 - 1=0\)).

Since the x - coordinate of each vertex increases by 3 (and the y - coordinate remains unchanged), the translation is 3 units to the right.

Answer:

C. 3 units to the right