Question

The map of a biking trail is drawn on a coordinate grid.

The trail starts at P(−2, 1) and goes to Q(6, 1).
It goes from Q to R(6, −3) and then to S(9, −3).

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

A. 11
B. 15
C. 18
D. 19

Answer 1

The distance from (-2,1) to (6,1) is 8 units

The distance from (6,1) to (6,-3) is 4 units

The distance from (6,-3) to (9,-3) is 3 units

Now add 'em up: 8 + 4 + 3 = 15

The length of the biking trail is 15 units long!

Hope that helps!

Answer 2

B. L=15 units

Explanation:

We have four points:

P(-2,1)

Q(6,1)

R(6,-3)

S(9,-3)

If you have two points
`A=(x_(1),y_(1)) , B=(x_(2),y_(2))` the distance between those points is the length of the segment that separates them. And the formula of that distance is:

`d(A,B)=√((x_2-x_1)^2+(y_2-y_1)^2)`

Then we have to calculate:

1. The distance between P and Q:

`d(P,Q)=√((6-(-2))^2+(1-1)^2)=√(8^2)=8`

2. The distance between Q and R:

`d(Q,R)=√((6-6)^2+(-3-1)^2)=√((-4)^2)=4`

3. The distance between R and S:

`d(R,S)=√((9-6)^2+(-3-(-3))^2)=√((3)^2)=3`

Then the total length of the biking trail is:

`L=d(P,Q)+d(Q,R)+d(R,S)\\L=8+4+3\\L=15 units`

The answer is:

B. L=15 units