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

Answer:

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

Step-by-step 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 = $\sqrt{(x_2 -x_1)^2 +(y_2-y_1)^2}$--------------(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 = $\sqrt{(6 -(-2))^2 +(1-1)^2}$

PQ = $\sqrt{(6 +2)^2 }$

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 = $\sqrt{(6 -6))^2 +((-3)- 1)^2}$

QR = $\sqrt{ (-4)^2}$

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= $\sqrt{(9 -6))^2 +(-3 -(-3))^2}$

RS = $\sqrt{ (3)^2}$

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