Question

in her lifeguarding class, summer swam a loop from point a to point b, then to point c and then diagonally back to point a. each unit on the graph represents 10 meters. if summer swam the loop 3 times, how many total meters did she swim? a. 120 meters (go to f) b. 210 meters (go to h) c. 360 meters (go to j) d. 400 meters (go to i)

Explanation:

Step1: Identify coordinates of points

Point A: $(3,8)$, Point B: $(3,4)$, Point C: $(6,4)$

Step2: Calculate distance A to B

Vertical distance: $|8-4|=4$ units

Step3: Calculate distance B to C

Horizontal distance: $|6-3|=3$ units

Step4: Calculate distance C to A

Use distance formula: $\sqrt{(6-3)^2+(4-8)^2}=\sqrt{3^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5$ units

Step5: Find 1-loop distance (units)

Sum: $4+3+5=12$ units

Step6: Convert 1-loop to meters

$12 \times 10 = 120$ meters

Step7: Calculate total distance (3 loops)

$120 \times 3 = 360$ meters

Answer:

C. 360 meters (go to J)