Question

use the insert shape options to place a dot on the coordinate plane. if needed, use a line to connect points. label the results with the letter assigned below.
a. draw the image of triangle abc under the transformation (x,y)→(x - 4,y + 1). label the result t.
b. draw the image of triangle abc under the transformation (x,y)→(-x,y). label the result r.

Explanation:

Step1: Identify coordinates of ABC

Let's assume \(A=(2,3)\), \(B=(4,2)\), \(C=(3,5)\) from the graph.

Step2: Find coordinates of \(T\) for transformation \((x,y)\to(x - 4,y + 1)\)

For point \(A\): \(x=2,y = 3\), new \(x=2-4=-2\), new \(y=3 + 1=4\), so \(A_T=(-2,4)\)
For point \(B\): \(x = 4,y=2\), new \(x=4-4 = 0\), new \(y=2+1=3\), so \(B_T=(0,3)\)
For point \(C\): \(x=3,y = 5\), new \(x=3-4=-1\), new \(y=5 + 1=6\), so \(C_T=(-1,6)\)

Step3: Find coordinates of \(R\) for transformation \((x,y)\to(-x,y)\)

For point \(A\): \(x = 2,y=3\), new \(x=-2\), new \(y = 3\), so \(A_R=(-2,3)\)
For point \(B\): \(x=4,y = 2\), new \(x=-4\), new \(y=2\), so \(B_R=(-4,2)\)
For point \(C\): \(x=3,y=5\), new \(x=-3\), new \(y=5\), so \(C_R=(-3,5)\)

Step4: Plot points

Plot points \(A_T,B_T,C_T\) and connect them to form triangle \(T\). Plot points \(A_R,B_R,C_R\) and connect them to form triangle \(R\) on the coordinate - plane.

Answer:

For part a: Plot points \(A_T(-2,4)\), \(B_T(0,3)\), \(C_T(-1,6)\) and connect them to get triangle \(T\).
For part b: Plot points \(A_R(-2,3)\), \(B_R(-4,2)\), \(C_R(-3,5)\) and connect them to get triangle \(R\).