The map of a biking trail is drawn on a coordinate grid. The trail starts at P(−7, 6) and goes to Q(4, 6). It goes from Q to R(4, −6) and then to S(6, −6). What is the total length (in units) of the biking trail?
25
12
13
21
I suggest you plot the points. You will find a bunch of horizontal and vertical line segments. Just add up the lengths.
To find the total length of the biking trail, we need to calculate the distances between each pair of consecutive points on the trail and then add them up.
Let's start by finding the distance between point P(−7, 6) and Q(4, 6). The formula to find the distance between two points (x1, y1) and (x2, y2) is:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
For P(-7, 6) and Q(4, 6), the distance is:
Distance = √((4 - (-7))^2 + (6 - 6)^2)
= √((4 + 7)^2 + (0)^2)
= √(11^2 + 0^2)
= √(121)
= 11
So, the distance between P and Q is 11 units.
Now, let's find the distance between Q(4, 6) and R(4, -6):
Distance = √((4 - 4)^2 + (-6 - 6)^2)
= √((0)^2 + (-12)^2)
= √(0 + 144)
= √144
= 12
The distance between Q and R is 12 units.
Finally, let's find the distance between R(4, -6) and S(6, -6):
Distance = √((6 - 4)^2 + (-6 - (-6))^2)
= √((2)^2 + (0)^2)
= √(4 + 0)
= √4
= 2
The distance between R and S is 2 units.
Now, we can add up the distances to find the total length of the biking trail:
Total Length = Distance(PQ) + Distance(QR) + Distance(RS)
= 11 + 12 + 2
= 25
Therefore, the total length of the biking trail is 25 units.