The map of a biking trail is drawn on a coordinate grid.
The trail starts at P(−3, 2) and goes to Q(1, 2).
It continues from Q to R(1, −1) and then to S(8, −1).
What is the total length (in units) of the biking trail?
11
13
14
16
You will have to use your distance formula three times.
Add the lengths of PQ , QR, and RS
I will do QR, you do the other distances , PQ and RS
Q(1,2), R(1,-1)
QR = √( (1-1)^2 + (-1-2)^2 )
= √( 0 + 9)
= 3 units
Just noticed that all your trips are either horizontal or vertical, so this is really easy.
Just count how far you have gone horizontally:
-3 ---> 8 which is 11 units
how far vertically:
2 ----> -1 , that is 3 units
so you have gone 11 units.
To find the length of the biking trail, we need to calculate the distance between each pair of consecutive points on the trail and then sum them up.
Let's calculate the distance between P(−3, 2) and Q(1, 2) first. The x-coordinates are 1 - (-3) = 4 units apart, but the y-coordinates are the same. So, the distance between P and Q is 4 units.
Next, we will calculate the distance between Q(1, 2) and R(1, −1). The x-coordinates are the same, but the y-coordinates are 2 - (-1) = 3 units apart. So, the distance between Q and R is 3 units.
Lastly, we will calculate the distance between R(1, −1) and S(8, −1). The y-coordinates are the same, but the x-coordinates are 8 - 1 = 7 units apart. So, the distance between R and S is 7 units.
To find the total length, we add up the distances: 4 units + 3 units + 7 units = 14 units.
Therefore, the total length of the biking trail is 14 units. Option C, 14, is the correct answer.
To find the total length of the biking trail, we need to calculate the sum of all the individual distances between the points on the trail.
Let's calculate the distances between each pair of consecutive points on the trail using the distance formula:
Distance between P and Q:
d(PQ) = √((x2 - x1)^2 + (y2 - y1)^2)
= √((1 - (-3))^2 + (2 - 2)^2)
= √((4)^2 + (0)^2)
= √(16)
= 4
Distance between Q and R:
d(QR) = √((x2 - x1)^2 + (y2 - y1)^2)
= √((1 - 1)^2 + (-1 - 2)^2)
= √((0)^2 + (-3)^2)
= √(9)
= 3
Distance between R and S:
d(RS) = √((x2 - x1)^2 + (y2 - y1)^2)
= √((8 - 1)^2 + (-1 - (-1))^2)
= √((7)^2 + (0)^2)
= √(49)
= 7
Now, let's find the total length of the biking trail by summing up these distances:
Total length = d(PQ) + d(QR) + d(RS)
= 4 + 3 + 7
= 14
Therefore, the total length of the biking trail is 14 units. So, the correct answer is 14.