Question

dr. lockhart is a large animal veterinarian. she has several farms that she visits once a month. the ziffel farm is 5 miles east and 15 miles south of her office. the douglas farm is 10 miles west and 5 miles north of her office. how far is the douglas farm from the ziffel farm?
a. 25 miles
b. 35 miles
c. 12.5 miles
d. 50 miles

Explanation:

Step1: Determine the coordinates

Let the office be at the origin \((0,0)\). The Ziffel Farm is at \((5,- 15)\) (east is positive \(x\)-direction and south is negative \(y\)-direction). The Douglas Farm is at \((-10,5)\) (west is negative \(x\)-direction and north is positive \(y\)-direction).

Step2: Use the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(x_1 = 5,y_1=-15,x_2=-10,y_2 = 5\).
First, find \((x_2 - x_1)\) and \((y_2 - y_1)\):
\(x_2-x_1=-10 - 5=-15\)
\(y_2 - y_1=5-(-15)=5 + 15 = 20\)
Then, \(d=\sqrt{(-15)^2+20^2}=\sqrt{225 + 400}=\sqrt{625}\)
\(\sqrt{625}=25\)

Answer:

A. 25 miles