Question

draw the preimage and image of each triangle under a translation along $\langle - 4,1\
angle$.

1. triangle with coordinates: $a(2,4)$, $b(1,2)$, $c(4,2)$.

transformation rule: $(x,y)\to$

Explanation:

Step1: Apply translation rule to each point

For a translation along \(\langle - 4,1
angle\), the rule is \((x,y)\to(x - 4,y + 1)\)
For point \(A(2,4)\):
\(x=2,y = 4\)
\(x-4=2-4=-2\)
\(y + 1=4 + 1=5\)
So \(A'\) is \((-2,5)\)

Step2: Apply translation rule to point \(B\)

For point \(B(1,2)\):
\(x = 1,y=2\)
\(x-4=1-4=-3\)
\(y + 1=2 + 1=3\)
So \(B'\) is \((-3,3)\)

Step3: Apply translation rule to point \(C\)

For point \(C(4,2)\):
\(x = 4,y=2\)
\(x-4=4-4=0\)
\(y + 1=2 + 1=3\)
So \(C'\) is \((0,3)\)

Answer:

Pre - image Coordinates \((x,y)\)	Image
\(B(1,2)\)	\(B'(-3,3)\)
\(C(4,2)\)	\(C'(0,3)\)