Question

practice problems:
use coordinate rules to find the coordinates of a b c after a transformation is applied to a triangle with coordinates a(3,-1), b(5,2), and c(6,-3).

1. translate abc 7 units left and 5 units up
2. reflect abc over the x - axis
3. reflect abc over the y - axis

Explanation:

Step1: Translate the points

For a translation \(7\) units left (\(x\) - coordinate: \(x-7\)) and \(5\) units up (\(y\) - coordinate: \(y + 5\)).
For point \(A(3,-1)\): \(x=3-7=-4\), \(y=-1 + 5=4\), new point \(A'(-4,4)\)
For point \(B(5,2)\): \(x=5-7=-2\), \(y=2 + 5=7\), new point \(B'(-2,7)\)
For point \(C(6,-3)\): \(x=6-7=-1\), \(y=-3 + 5=2\), new point \(C'(-1,2)\)

Step2: Reflect over the \(x\) - axis

The rule for reflection over the \(x\) - axis is \((x,y)\to(x,-y)\)
For point \(A(3,-1)\): new point \(A''(3,1)\)
For point \(B(5,2)\): new point \(B''(5,-2)\)
For point \(C(6,-3)\): new point \(C''(6,3)\)

Step3: Reflect over the \(y\) - axis

The rule for reflection over the \(y\) - axis is \((x,y)\to(-x,y)\)
For point \(A(3,-1)\): new point \(A'''(-3,-1)\)
For point \(B(5,2)\): new point \(B'''(-5,2)\)
For point \(C(6,-3)\): new point \(C'''(-6,-3)\)

Answer:

1. \(A'(-4,4)\), \(B'(-2,7)\), \(C'(-1,2)\)
2. \(A''(3,1)\), \(B''(5,-2)\), \(C''(6,3)\)
3. \(A'''(-3,-1)\), \(B'''(-5,2)\), \(C'''(-6,-3)\)