Question

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

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

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 x - coordinate change

For point \( A(-4,3) \) to \( A'(-1,3) \), the change in \( x \)-coordinate is \( - 1-(-4)=3 \). For point \( B(0,4) \) to \( B'(3,4) \), the change in \( x \)-coordinate is \( 3 - 0=3 \). For point \( C(-3,1) \) to \( C'(0,1) \), the change in \( x \)-coordinate is \( 0-(-3) = 3 \). The \( y \)-coordinate remains the same for all points (\( 3
ightarrow3 \), \( 4
ightarrow4 \), \( 1
ightarrow1 \)).

Step2: Determine translation direction

Since the \( x \)-coordinate increases by 3 and \( y \)-coordinate is unchanged, the translation is 3 units to the right (because moving right on the coordinate plane increases the \( x \)-coordinate).

Answer:

3 units to the right