Question

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). What is the total length (in units) of the biking trail? (1 point)

9


12


16


19

Answer 1

The answer is D. 19. The total length of the biking trial is 19.

Answer 2

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

`d=√((c-a)^2+(d-b)^2).`

So, the length of the line segments PQ, QR and RS are given by

`PQ=√((3+6)^2+(3-3)^2)=√(9^2+0^2)=√(9^2)=9,\\\\\\QR=√((3-3)^2+(-4-3)^2)=√(0^2+7^2)=√(7^2)=7,\\\\\\RS=√((6-3)^2+(-4+4)^2)=√(3^2+0^2)=√(3^2)=3.`

Therefore, the total length of the biking trail is given by

`\ell=PQ+QR+RS=9+7+3=19~\textup{units}.`

Thus, the total length of the biking trail is 19 units.

Option (D) is CORRECT.