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

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

$d=\sqrt{(c-a)^2+(d-b)^2}.$

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

$PQ=\sqrt{(3+6)^2+(3-3)^2}=\sqrt{9^2+0^2}=\sqrt{9^2}=9,\\\\\\QR=\sqrt{(3-3)^2+(-4-3)^2}=\sqrt{0^2+7^2}=\sqrt{7^2}=7,\\\\\\RS=\sqrt{(6-3)^2+(-4+4)^2}=\sqrt{3^2+0^2}=\sqrt{3^2}=3.$

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.

Answer 2

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