Question

1. a triangle has vertices ( a(1,2), b(3,4) ), and ( c(2,6) ). after a transformation, the vertices become ( a^{prime}(4,5), b^{prime}(6,7) ), and ( c^{prime}(5,9) ). what is the translation rule?

( \bigcirc ) a. ( (x + 3, y+3) )
( \bigcirc ) b. ( (x - 3, y+2) )
( \bigcirc ) c. ( (x + 3, y-3) )
( \bigcirc ) d. ( (x + 2, y+3) )

Explanation:

Step1: Calculate the change in x - coordinate

For point \(A(1,2)\) and \(A'(4,5)\), the change in \(x\) is \(4 - 1=3\). For point \(B(3,4)\) and \(B'(6,7)\), the change in \(x\) is \(6 - 3 = 3\). For point \(C(2,6)\) and \(C'(5,9)\), the change in \(x\) is \(5 - 2=3\).

Step2: Calculate the change in y - coordinate

For point \(A(1,2)\) and \(A'(4,5)\), the change in \(y\) is \(5 - 2 = 3\). For point \(B(3,4)\) and \(B'(6,7)\), the change in \(y\) is \(7 - 4=3\). For point \(C(2,6)\) and \(C'(5,9)\), the change in \(y\) is \(9 - 6 = 3\).

The translation rule is \((x,y)\to(x + 3,y+3)\)

Answer:

a. \((x + 3,y + 3)\)