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

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 = --------------(1)

Step 1: Distance between PQ

Here

Substituting the values in eq(1)

PQ =

PQ =

PQ =

PQ = 8

Step 2: Distance between QR

Here

Substituting the values in eq(1)

QR =

QR =

QR =

QR = 4

Step 3: Distance between RS

Here

Substituting the values in eq(1)

RS=

RS =

RS =

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

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°