Question

tyrek is planning the location for a farmers market using a map of his community. tyrekes community map tyreke wants the farmers market to be near the park and far from the store. which point on the map would be a good location for the farmers market? (a) (0, 1) (b) (2, 4) (c) (5, 2) (d) (6, 0)

Explanation:

Step1: Identify park and store coordinates

The park is at (1, 2) and the store is at (3, 4).

Step2: Calculate distances to each option

• For option a (0, 1): Distance to park $d_{park - a}=\sqrt{(1 - 0)^2+(2 - 1)^2}=\sqrt{1 + 1}=\sqrt{2}$; Distance to store $d_{store - a}=\sqrt{(3 - 0)^2+(4 - 1)^2}=\sqrt{9 + 9}=\sqrt{18}=3\sqrt{2}$.
• For option b (2, 4): Distance to park $d_{park - b}=\sqrt{(2 - 1)^2+(4 - 2)^2}=\sqrt{1+4}=\sqrt{5}$; Distance to store $d_{store - b}=\sqrt{(3 - 2)^2+(4 - 4)^2}=1$.
• For option c (5, 2): Distance to park $d_{park - c}=\sqrt{(5 - 1)^2+(2 - 2)^2}=4$; Distance to store $d_{store - c}=\sqrt{(5 - 3)^2+(2 - 4)^2}=\sqrt{4 + 4}=2\sqrt{2}$.
• For option d (6, 0): Distance to park $d_{park - d}=\sqrt{(6 - 1)^2+(0 - 2)^2}=\sqrt{25 + 4}=\sqrt{29}$; Distance to store $d_{store - d}=\sqrt{(6 - 3)^2+(0 - 4)^2}=\sqrt{9 + 16}=5$.

Step3: Compare distances

We want a point near the park and far from the store. Option a has a relatively small distance to the park and a relatively large distance to the store compared to other options.

Answer:

A. (0, 1)