Question

The map of a walking trail is drawn on a coordinate grid with three points of interest. The trail starts at R(−3, 2) and goes to S(2, 2) and continues to T(2, −5). The total length of the walking trail is ____ units. (Input whole numbers only.)

Answer 1

Answer:12 units

Step-by-step explanation:

Point R is (-3,2) and point S is (2,2)

distance between them is

RS=$\sqrt{5^2+0^2}$=5

ST=$\sqrt{7^2+0^2}$=7

Total distance is RS+ST=5+7=12 units

Answer 2

Answer

Find out the the total length of the walking trail .

To prove

Formula

$Distance\ formula = \sqrt{(x_{2} - x_{1})^{2} +( y_{2} - y_{1})^{2}}$

As given

The trail starts at R(−3, 2) and goes to S(2, 2) and continues to T(2, −5).

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

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

$RS = \sqrt{5^{2}}$

$RS = \sqrt{25}$

$\sqrt{25} = 5$

RS = 5 units

As given

S(2, 2) and continues to T(2, −5).

Now

$ST = \sqrt{(2-2)^{2} +( -5-2 )^{2}}$

$ST = \sqrt{( - 7)^{2}}$

$ST = \sqrt{49}$

$\sqrt{49} = 7$

ST = 7 units

Therefore

Total length of the trail = RS + ST

                                      =  5 units + 7 units

                                      = 12 units

Therefore the total length of the trail is 12 units.