Question

1. the image of ( a(-3,-5) ) under a translation is ( a(6,-1) ). find the image of ( b(3,-2) ) under the same translation.
2. explain why ( \triangle abc ) with vertices ( a(-1,-2), b(0,0) ), and ( c(-6,0) ) is not a translation image of ( \triangle abc ) with vertices ( a(1,2), b(0,0) ), and ( c(6,0) ). hint: graph it!

Explanation:

Step1: Find the translation rule

For a point \((x,y)\) translated to \((x',y')\), the rule is \((x',y')=(x + a,y + b)\). Given \(A(-3,-5)\) and \(A'(6,-1)\), we have:
\(6=-3 + a\) and \(-1=-5 + b\)
Solve for \(a\) and \(b\):
\(a = 6-(-3)=9\)
\(b=-1-(-5)=4\)
The translation rule is \((x,y)\to(x + 9,y + 4)\)

Step2: Apply the translation rule to point \(B\)

For \(B(3,-2)\), using the rule \((x,y)\to(x + 9,y + 4)\)
\(x'=3 + 9=12\)
\(y'=-2 + 4=2\)

Answer:

The image of \(B(3,-2)\) is \((12,2)\)