Answer :
Answer: The correct option is (D) 19.
Step-by-step explanation: Given that the map of a biking trail is drawn on a coordinate grid.
The trail starts at P(−6, 3) and goes to Q(3, 3). It goes from Q to R(3, −4) and then to S(6, −4).
We are to find the total length in units of the biking trail.
The length of a line segment is equal to the distance between the endpoints of the segment.
Distance formula :
The distance between two points (a, b) and (c, d) is given by
[tex]d=\sqrt{(c-a)^2+(d-b)^2}.[/tex]
So, the length of the line segments PQ, QR and RS are given by
[tex]PQ=\sqrt{(3+6)^2+(3-3)^2}=\sqrt{9^2+0^2}=\sqrt{9^2}=9,\\\\\\QR=\sqrt{(3-3)^2+(-4-3)^2}=\sqrt{0^2+7^2}=\sqrt{7^2}=7,\\\\\\RS=\sqrt{(6-3)^2+(-4+4)^2}=\sqrt{3^2+0^2}=\sqrt{3^2}=3.[/tex]
Therefore, the total length of the biking trail is given by
[tex]\ell=PQ+QR+RS=9+7+3=19~\textup{units}.[/tex]
Thus, the total length of the biking trail is 19 units.
Option (D) is CORRECT.