Question

question #15 (2 points) g.gsr.3.3 given △cat, identify a translation that will map △cat to another quadrant (not on an axis). write the rule and perform the translation. label the vertices of the image.

Explanation:

Step1: Select a translation rule

Choose \((x,y)\to(x - 7,y + 6)\) to move the triangle to another quadrant.

Step2: Apply rule to vertex C

If \(C=(3,3)\), then \(C'=(3-7,3 + 6)\)

Step3: Apply rule to vertex A

If \(A=(4,7)\), then \(A'=(4-7,7 + 6)\)

Step4: Apply rule to vertex T

If \(T=(5,1)\), then \(T'=(5-7,1 + 6)\)

Answer:

Let's assume the vertices of \(\triangle CAT\) have coordinates \(C(x_1,y_1)\), \(A(x_2,y_2)\), \(T(x_3,y_3)\). A possible translation rule to move the triangle to another quadrant is \((x,y)\to(x - 5,y - 5)\).
If \(C=(3,3)\), \(A=(4,7)\), \(T=(5,1)\)
The new - coordinates of \(C'\) are \((3 - 5,3 - 5)=(- 2,-2)\)
The new - coordinates of \(A'\) are \((4 - 5,7 - 5)=(-1,2)\)
The new - coordinates of \(T'\) are \((5 - 5,1 - 5)=(0,-4)\) (this point is on the y - axis, so let's choose another rule).
Let the translation rule be \((x,y)\to(x+6,y - 7)\)
If \(C=(3,3)\), then \(C'=(3 + 6,3-7)=(9,-4)\)
If \(A=(4,7)\), then \(A'=(4 + 6,7 - 7)=(10,0)\) (on the x - axis, wrong choice).
Let the translation rule be \((x,y)\to(x - 7,y+6)\)
If \(C=(3,3)\), then \(C'=(3-7,3 + 6)=(-4,9)\)
If \(A=(4,7)\), then \(A'=(4-7,7 + 6)=(-3,13)\)
If \(T=(5,1)\), then \(T'=(5-7,1 + 6)=(-2,7)\)
The translation rule is \((x,y)\to(x - 7,y + 6)\) and the vertices of the image \(\triangle C'A'T'\) are \(C'(-4,9)\), \(A'(-3,13)\), \(T'(-2,7)\)