Question

in the figure below, △abc has vertices a(1,1), b(4,1), and c(4,5). △abc is first translated 5 units to the left and 2 units up followed by a reflection over the line y = 1.
a) a(6,3) b(9,3) c(9,7)
b) a(-6,3) b(-9,3) c(-9,7)
c) a(-6,-3) b(-9,-3) c(-9,-7)
d) a(6,-3) b(9,-3) c(9,-7)

Explanation:

Step1: Translation rule

Translation to the right by \(5\) units and up by \(2\) units has the rule \((x,y)\to(x + 5,y+2)\). For point \(A(1,1)\), after translation, \(A'=(1 + 5,1+2)=(6,3)\); for \(B(4,1)\), \(B'=(4 + 5,1+2)=(9,3)\); for \(C(4,5)\), \(C'=(4 + 5,5+2)=(9,7)\).

Step2: Reflection rule

Reflection over the line \(y = 1\) has the rule \((x,y)\to(x,2 - y)\). For \(A'(6,3)\), \(A''=(6,2 - 3)=(6,- 3)\); for \(B'(9,3)\), \(B''=(9,2 - 3)=(9,-3)\); for \(C'(9,7)\), \(C''=(9,2 - 7)=(9,-7)\)

Answer:

D. \(A''(6,-3)\), \(B''(9,-3)\), \(C''(9,-7)\)