Question

in the figure of right - triangle abc with a(2,8) b(6,1) c(2,3). a. graph the line x = y. b. reflect △abc across the line x = y creating a new triangle abc. label it clearly and list the coordinates of the image. c. rotate △abc 90° counter - clockwise about the origin creating a new triangle abc. label it clearly and list the coordinates of the image. d. translate △abc to △abc according to the rule: (x,y)→(x + 5,y - 2). a______ b____ c______ e. of the triangles now on the three graphs, which has the largest area?

Explanation:

Step1: Apply translation rule to point A

Given \(A(2,4)\), for the rule \((x,y)\to(x + 5,y - 2)\), substitute \(x = 2\) and \(y=4\). We get \(x'=2 + 5=7\) and \(y'=4- 2 = 2\). So \(A'''=(7,2)\)

Step2: Apply translation rule to point B

Given \(B(4,1)\), substitute \(x = 4\) and \(y = 1\) into the rule \((x,y)\to(x + 5,y - 2)\). We have \(x'=4+5 = 9\) and \(y'=1 - 2=-1\). So \(B'''=(9,-1)\)

Step3: Apply translation rule to point C

Given \(C(2,3)\), substitute \(x = 2\) and \(y = 3\) into the rule \((x,y)\to(x + 5,y - 2)\). We obtain \(x'=2+5 = 7\) and \(y'=3 - 2=1\). So \(C'''=(7,1)\)

Answer:

\(A'''(7,2)\), \(B'''(9,-1)\), \(C'''(7,1)\)