Answer:
√689 ≈ 26.2 leagues
Explanation:
For the purpose of calculating the distance between the marked points, the line is considered to be the hypotenuse of a right triangle. The horizontal distance between the points is one leg of the triangle, and the vertical distance is the other leg. The Pythagorean theorem relates these distances.
Pythagorean relation
The Pythagorean theorem relates right triangle sides 'a' and 'b' to hypotenuse 'c' with the formula ...
c² = a² +b²
Taking the square root, we have an expression for 'c' in terms of 'a' and 'b'.
c = √(a² +b²)
Application to distance
The horizontal distance between the points is the difference of their x-coordinates:
a = x2 -x1 = 2 -(-18) = 20
The vertical distance between the points is the difference of their y-coordinates:
b = y2 -y1 = -10 -7 = -17
When we square these numbers, we find their signs to be irrelevant.
c = √(a² +b²) = √(20² +(-17)²) = √(400 +289) = √689
c ≈ 26.249
The distance between the given points is about 26.2 leagues.