Question

question 1 - 4
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.
( square (x,y)\to(x + 3,y - 2) )
( square (x,y)\to(x - 3,y + 2) )
( square (x,y)\to(x - 2,y + 3) )
( square (x,y)\to(x + 2,y - 3) )
( square ) triangle ( abc ) translates 3 units to the left and 2 units up
( square ) triangle ( abc ) translates 2 units to the right and 3 units down

Explanation:

Step1: Analyze the change in \(x -\)coordinates

For point \(A(-3,0)\) and \(A'(-6,2)\): \(-6-(-3)=- 3\).
For point \(B(-1,0)\) and \(B'(-4,2)\): \(-4 - (-1)=-3\).
For point \(C(-3,-4)\) and \(C'(-6,-2)\): \(-6-(-3)=-3\).
The change in \(x -\)coordinate is \(x\to x - 3\).

Step2: Analyze the change in \(y -\)coordinates

For point \(A(-3,0)\) and \(A'(-6,2)\): \(2 - 0=2\).
For point \(B(-1,0)\) and \(B'(-4,2)\): \(2 - 0=2\).
For point \(C(-3,-4)\) and \(C'(-6,-2)\): \(-2-(-4)=2\).
The change in \(y -\)coordinate is \(y\to y + 2\).
The transformation rule is \((x,y)\to(x - 3,y + 2)\).
In terms of translation, moving \(3\) units to the left (because \(x\) - value decreases by \(3\)) and \(2\) units up (because \(y\) - value increases by \(2\))

Answer:

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