Question

the surry county sheriffs patrol route starts in coby. the composition of rigid motions t⟨-20,10⟩ ∘ t⟨40, -50⟩ describes her route. describe the sheriffs route in words.

the sheriff drives miles and miles from coby to then she drives miles and miles to
(type whole numbers.)

Explanation:

Step1: Analyze the first translation \( T_{\langle -20,10

angle} \)
A translation \( T_{\langle a,b
angle} \) means moving \( a \) units horizontally (negative for left, positive for right) and \( b \) units vertically (negative for down, positive for up). For \( T_{\langle -20,10
angle} \), this is moving 20 miles left and 10 miles up. Starting from Coby, this should take to Byder (checking the graph's coordinates: Coby to Byder, left 20 (since x - 20) and up 10 (y + 10)).

Step2: Analyze the second translation \( T_{\langle 40,-50

angle} \)
For \( T_{\langle 40,-50
angle} \), this is moving 40 miles right and 50 miles down. From Byder, moving right 40 and down 50 should lead to the next point (looking at the graph, from Byder, right 40 (x + 40) and down 50 (y - 50) would take to the next patrol point, likely the final or another, but the route is Coby -> Byder (via \( T_{\langle -20,10
angle} \)) then Byder -> next (via \( T_{\langle 40,-50
angle} \)).

Step3: Describe the route

First, from Coby, the sheriff drives 20 miles left (since -20 in x) and 10 miles up (since +10 in y) to Byder. Then, from Byder, drives 40 miles right (since +40 in x) and 50 miles down (since -50 in y) to the next location (could be part of the patrol, like towards the lower - right points like Logan/Medon/Dallinger area).

Answer:

The sheriff drives 20 miles left and 10 miles up from Coby to Byder. Then she drives 40 miles right and 50 miles down from Byder to the next patrol location.