Question

The map of a biking trail is drawn on a coordinates grid

The tiail 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



`11`

`15`

`18`

`19`
​

Answer 1

The total length (in units) of the biking trail is 15 units

Explanation:

Given:

P = (-2,1)

Q = (6, 1)

R = (6,-3)

s = (9,-3)

To Find:

The total length (in units) of the biking trail = ?

Solution:

Distance between two points can be found by the

d =
`√((x_2 -x_1)^2 +(y_2-y_1)^2)`--------------(1)

Step 1: Distance between PQ

Here

`x_1 = -2 \\ y_1 = 1\\x_2 = 6 \\ y_2 = 1`

Substituting the values in eq(1)

PQ =
`√((6 -(-2))^2 +(1-1)^2)`

PQ =
`√((6 +2)^2 )`

PQ =
`\sqrt{8^2`

`PQ = \sqrt{64`

PQ = 8

Step 2: Distance between QR

Here

`x_1 = 6 \\ y_1 = 1\\x_2 = 6 \\ y_2 = -3`

Substituting the values in eq(1)

QR =
`√((6 -6))^2 +((-3)- 1)^2)`

QR =
`√( (-4)^2)`

QR =
`\sqrt{16`

QR = 4

Step 3: Distance between RS

Here

`x_1 = 6 \\ y_1 = -3\\x_2 = 9 \\ y_2 = -3`

Substituting the values in eq(1)

RS=
`√((9 -6))^2 +(-3 -(-3))^2)`

RS =
`√( (3)^2)`

RS =
`\sqrt{9`

RS = 3

Step 4: Finding the total distance of the trail

The total distance of the biking trail is = PQ + QR + RS

=> 8+4+3

=> 15