Question

Gabriela uses two mist nets to catch songbirds to study. Songbirds are captured and taken to a banding station. She then measures each bird before freeing the bird with a band on the right leg.

The banding station is 0.6 mi due east from the bunkhouse. The first net is 0.8 mi due north of the banding station. The second net is northwest of the banding station. Gabriela and her helpers walk the following loop to collect the birds from the nets.
They walk from the banding station directly to the first net. From the first net, they go 0.5 mi north to the boundary of a park and then go 0.9 mi due west, where they are due north of the second net. They go due south to the second
net and then return directly to the banding station along a straight line southeast.

Use the coordinate grid with the distance between lines equal to 0.1 mi. Plot the loop. Mark and label each location, and use arrow marks to show the direction.
2. The loop makes a polygon. What is the polygon? Give the most precise description. Explain.
3. What distance is a single loop from the banding station to the two nets and back? Round your answer to the nearest 0.1 mi.
4. After her first time around the loop, Gabriela leaves the banding station
and walks the loop in reverse to the first net. Then she walks from the first net along a straight line to the bunkhouse. How far does she walk from the banding station to the bunkhouse? Round your answer to the nearest 0.1 mi.

Answer 1

This is a multi-part question. Let’s start with the first part. To plot the loop on a coordinate grid, we can use the information given to determine the coordinates of each location. Let’s assume that the banding station is at the origin (0,0). Since it is 0.6 mi due east from the bunkhouse, we can place the bunkhouse at (-0.6, 0). The first net is 0.8 mi due north of the banding station, so its coordinates are (0, 0.8). From the first net, Gabriela and her helpers go 0.5 mi north to the boundary of a park and then go 0.9 mi due west, where they are due north of the second net. This means that the second net is located at (-0.9, 0.8). From there, they return directly to the banding station along a straight line southeast.

Explanation: