Question

you walk along the outside of a park starting at point p to point q. then you take a shortcut back to point p, represented by (overline{pq}) on the graph. use the accompanying graph to answer parts a and b.
click the icon to view the graph.

a. what is the length of the shortcut in m
the length of the shortcut is (square) mi.
(round to the nearest tenth as needed.)

Explanation:

Step1: Identify coordinates of P and Q

Point \( P \) is at \( (0, 0) \) and point \( Q \) is at \( (1.2, 1.6) \).

Step2: Apply distance formula

The distance formula between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).
Substituting \( x_1 = 0, y_1 = 0, x_2 = 1.2, y_2 = 1.6 \):
\[
d = \sqrt{(1.2 - 0)^2 + (1.6 - 0)^2} = \sqrt{1.44 + 2.56} = \sqrt{4} = 2.0
\]

Answer:

2.0