Question

a triangle has vertices at ( a(2,3) ). ( b(5,7) ), and ( c(7,4) ). which will be the coordinates of these vertices after translating the triangle 3 units left and 2 units up? ( a(-1,5), b(2,9), c(4,6) ) ( a(5,1), b(8,5), c(10,2) ) ( a(-1,1), b(2,5), c(4,2) ) ( a(5,5), b(8,9), c(10,6) )

Explanation:

Step1: Determine the translation rule

Translating 3 units left means subtracting 3 from the \(x -\)coordinate. Translating 2 units up means adding 2 to the \(y -\)coordinate. The rule is \((x,y)\to(x - 3,y + 2)\).

Step2: Apply the rule to point \(A(2,3)\)

For \(A(2,3)\):
\(x=2,y = 3\)
\(x-3=2-3=-1\)
\(y + 2=3+2 = 5\)
So \(A'\) is \((-1,5)\)

Step3: Apply the rule to point \(B(5,7)\)

For \(B(5,7)\):
\(x = 5,y=7\)
\(x-3=5 - 3=2\)
\(y + 2=7+2=9\)
So \(B'\) is \((2,9)\)

Step4: Apply the rule to point \(C(7,4)\)

For \(C(7,4)\):
\(x=7,y = 4\)
\(x-3=7-3=4\)
\(y + 2=4+2=6\)
So \(C'\) is \((4,6)\)

Answer:

\(A'(-1,5),B'(2,9),C'(4,6)\) (the first option)