Question

1. triangle ( a b c ) with vertices ( a(6,7), b(7,3) ), and ( c(1,4):(x, y)

ightarrow(x - 3, y - 6) )

1. rectangle ( d e f g ) with vertices ( d(-4,3), e(0,2) ), ( f(-2,-6) ), and ( g(-6,-5):(x, y)

ightarrow(x + 4, y + 1) )
6.

Explanation:

Step1: For triangle \(ABC\) with translation \((x,y)\to(x - 3,y-4)\)

• For point \(A(6,7)\):

\(x'=6 - 3=3\), \(y'=7-4 = 3\), so \(A'(3,3)\)

• For point \(B(7,3)\):

\(x'=7 - 3=4\), \(y'=3-4=-1\), so \(B'(4,-1)\)

• For point \(C(1,4)\):

\(x'=1 - 3=-2\), \(y'=4-4 = 0\), so \(C'(-2,0)\)

Step2: For rectangle \(DEFG\) with translation \((x,y)\to(x + 4,y + 1)\)

• For point \(D(-4,3)\):

\(x'=-4+4 = 0\), \(y'=3 + 1=4\), so \(D'(0,4)\)

• For point \(E(0,2)\):

\(x'=0+4 = 4\), \(y'=2 + 1=3\), so \(E'(4,3)\)

• For point \(F(-2,-6)\):

\(x'=-2+4 = 2\), \(y'=-6 + 1=-5\), so \(F'(2,-5)\)

• For point \(G(-6,-5)\):

\(x'=-6+4=-2\), \(y'=-5 + 1=-4\), so \(G'(-2,-4)\)

Step3: For the general translation in 6

The rule of translation is \((x,y)\to(x,y - 6)\) (by observing the vertical shift of points \(P\to P'\), \(Q\to Q'\), \(R\to R'\))

Answer:

• For triangle \(ABC\): \(A'(3,3)\), \(B'(4,-1)\), \(C'(-2,0)\)
• For rectangle \(DEFG\): \(D'(0,4)\), \(E'(4,3)\), \(F'(2,-5)\), \(G'(-2,-4)\)
• For 6: The rule is \((x,y)\to(x,y - 6)\)