Question

what is the composition of translations ((t_{<-3,4>} circ t_{<8,-7>})) written as one translation? (\bigcirc) (t_{<-5,3>}) (\bigcirc) (t_{<-24,-28>}) (\bigcirc) (t_{<5,-3>}) (\bigcirc) (t_{<11,11>})

Explanation:

Step1: Recall translation composition rule

For translations \( T_{\langle a,b
angle} \) and \( T_{\langle c,d
angle} \), the composition \( T_{\langle a,b
angle} \circ T_{\langle c,d
angle} \) is given by \( T_{\langle a + c, b + d
angle} \).

Step2: Identify the components

Here, \( T_{\langle -3,4
angle} \circ T_{\langle 8,-7
angle} \), so \( a=-3 \), \( b = 4 \), \( c = 8 \), \( d=-7 \).

Step3: Calculate the new components

Calculate the \( x \)-component: \( -3+8 = 5 \)
Calculate the \( y \)-component: \( 4+(-7)=4 - 7=-3 \)

So the composition is \( T_{\langle 5,-3
angle} \).

Answer:

\( T_{\langle 5,-3
angle} \) (corresponding to the option \( T_{\langle 5,-3
angle} \))