Question

A camper leaves camp on a kayak and travels 50 miles east on a river, then he ties his kayak to the bank and travels 20 miles north on a bicycle. This trip can be plotted on the coordinate plane, where the camp is the point (0, 0). The distant of the camper to the camp can be found using the distance formula. Which other formula can he use?

Answer 1

I think the Pythagorean Theorem Formula also thinks. 

Answer 2

Answer:

53.85 miles

Step-by-step explanation:

the camp is the point (0, 0)

Camper travels 50 miles east on a river, then he ties his kayak to the bank

If he travels 50 miles east then he reaches the point (50,0) on coordinate plane. He travels 20 miles north from the point (50,0)

If he travels 20 miles up from the point (50,0) then he reaches the point

(50, 20) on coordinate plane

Now we find the distance between (0,0) and (50,20)

The diagram is attached below

Distance D = $\sqrt{(x_2-x_1)^2+(y_2-y_2)^2}$

= $\sqrt{(50-0)^2+(20-0)^2}$

= $\sqrt{(50)^2+(20)^2}$

= $\sqrt{(2500)^2+(400)^2}$

= $\sqrt{2900}$

= 53. 85

Distance = 53.85 miles

We can use Pythagorean theorem

AC^2 = AB^2 + BC^2

$AC^2= 50^2 + 20^2 = 2500 + 400 = 2900$

$AC = \sqrt{2900} =53. 85 miles$