c) Knowing Tony is injured, they need to travel the shortest distance possible back to a road. They are located at (4,11), towards which road should they head and how far will they need to walk to reach this road?
here's a picture of the previous information: imgur.com/a/2XvRQW4
line A: 2x+3y+12 = 0
The distance from (4,11) to Line A is thus
|2*4 + 3*11 + 12|/√(2^2+3^2) = 53/√13
Now do the same calculation with Line B and choose the one you want.
To determine the shortest distance for Tony to travel back to a road, we need to identify the nearest road to his current location at (4,11). However, since the picture you mentioned is not accessible to me, I will guide you through a step-by-step approach to find the answer.
1. Identify the road network: Determine the roads available in the vicinity of Tony's location. Roads are typically represented by lines on a map or a grid.
2. Calculate distances: Measure the Euclidean distance between Tony's location and each nearby road. The Euclidean distance represents the straight-line distance between two points. The formula to calculate it is:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this formula, (x1, y1) represent Tony's location, and (x2, y2) represent the coordinates of each road.
3. Select the nearest road: Compare the distances calculated in the previous step to find the road that is closest to Tony's location.
By following these steps and having access to the road network, you should be able to determine the direction Tony should head and the distance he needs to walk to reach the nearest road.