A doctor drives from her home, located 2 miles east and 20 miles north of town to her courthouse office, located 5 miles west and 4 miles south of her town courthouse. What is the between the...

A doctor drives from her home, located 2 miles east and 20 miles north of town to her courthouse office, located 5 miles west and 4 miles south of her town courthouse. What is the between the doctor's home and office? 

Asked on by monique06

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The doctor drives from her home, located 2 miles east and 20 miles north of town to her courthouse office, located 5 miles west and 4 miles south of her town courthouse.

Let the point representing the courthouse have the coordinates (0, 0), and the x and y axes lie along the North and East directions respectively. The coordinates of the doctor's house are (2, 20) and that of her office are (-5, -4)

The distance between the points (2, 20) and (-5, -4) is `D = sqrt((2 + 5)^2 + (20 + 4)^2)`

= `sqrt(49+576)`

= `sqrt 625`

= 25

The distance between the doctor's home and her office is 25 miles.

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