Question

question 1-1
triangle abc with coordinates a(-3,0), b(-1,0), and c(-3,-4) was transformed to create triangle abc with coordinates a(-6,2), b(-4,2), and c(-6,-2). describe the transformation of triangle abc to triangle abc. select all that apply
□ (x,y) → (x + 3, y - 2)
□ (x,y) → (x - 3, y + 2)
□ (x,y) → (x - 2, y + 3)
□ (x,y) → (x + 2, y - 3)
□ triangle abc translates 3 units to the left and 2 units up
□ triangle abc translates 2 units to the right and 3 units down

Explanation:

Step1: Analyze x - coordinate transformation

Take point \( A(-3,0) \) to \( A'(-6,2) \). The change in \( x \)-coordinate: \( -6-(-3)=-3 \), so \( x \) changes by \( - 3 \) (i.e., \( x-3 \)).
Take point \( B(-1,0) \) to \( B'(-4,2) \). The change in \( x \)-coordinate: \( -4 - (-1)=-3 \), so \( x \) changes by \( -3 \) (i.e., \( x - 3 \)).
Take point \( C(-3,-4) \) to \( C'(-6,-2) \). The change in \( x \)-coordinate: \( -6-(-3)=-3 \), so \( x \) changes by \( -3 \) (i.e., \( x - 3 \)).

Step2: Analyze y - coordinate transformation

Take point \( A(-3,0) \) to \( A'(-6,2) \). The change in \( y \)-coordinate: \( 2 - 0=2 \), so \( y \) changes by \( + 2 \) (i.e., \( y + 2 \)).
Take point \( B(-1,0) \) to \( B'(-4,2) \). The change in \( y \)-coordinate: \( 2-0 = 2 \), so \( y \) changes by \( +2 \) (i.e., \( y + 2 \)).
Take point \( C(-3,-4) \) to \( C'(-6,-2) \). The change in \( y \)-coordinate: \( -2-(-4)=2 \), so \( y \) changes by \( +2 \) (i.e., \( y + 2 \)).

Step3: Match with transformation rules

The transformation rule is \( (x,y)\to(x - 3,y + 2) \), which means translating 3 units to the left (since \( x \) decreases by 3) and 2 units up (since \( y \) increases by 2).

Answer:

\( (x,y)\to(x - 3,y + 2) \), Triangle ABC translates 3 units to the left and 2 units up