Question

Find the distance between the following
two coordinates:

(-5, 3) and (-9, 5)

Answer 1

`√([-9-(-5)]^2+ (5-3)^2) =\\\\\\√((-9+5)^2+(2)^2) = √(4^2+2^2) = √(20)`

distance between the two coordinates: √20

Explanation:

Answer 2

2√5 ≈ 4.472

Explanation:

You want the distance between the points at coordinates (-5, 3) and (-9, 5).

Distance formula

The distance formula can be used to find the distance of interest:

d = √((x2 -x1)² +(y2 -y1)²)

d = √((-9 -(-5))² +(5 -3)²) = √((-4)² +2²) = √(16 +4)

d = √20 = √(4·5) = 2√5

The distance between the points is 2√5, about 4.472 units.

Calculator

Modern calculators have a number of functions that can be used to find the distance between two points. These include complex number operations and vector operations, as shown in the attached calculator display. The vector between the points is found as the difference of the corresponding coordinates:

(-9 -(-5), 5 -3) = (-4, 2)

The magnitude of that vector is the root of the sum of the squares of its components, as found by the distance formula. When the vector is written as a complex number, that magnitude is its "absolute value." The magnitude is also the "norm" of that vector.

The distance is 2√5 ≈ 4.472 units.