Question

Calculate the distance between the points c=, (2,−2) and p=( 7,−6) in the coordinate plane.

Give an exact answer (not a decimal approximation).

d= square root of: (x₂-x₁)² + (y₂-y₁)²
answer is the square root of ____

Answer 1

The distance between the points c=(2, -2) and p=(7, -6) is found using the distance formula, which results in √41 units as the exact answer.

Step-by-step explanation:

To calculate the distance between two points c = (2, −2) and p = (7, −6) in the coordinate plane, we use the distance formula:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Substitute the given coordinates into the formula:

x₁ = 2, y₁ = −2

x₂ = 7, y₂ = −6

Proceed with the calculation:

d = √((7 - 2)² + (−6 - (−2))²)

d = √(5² + (−4)²)

d = √(25 + 16)

d = √41

Therefore, the exact distance between the points is √41 units.

Distance is the measure of how far apart two points or objects are, typically in terms of space or time. In a physical sense, it's the amount of space between two locations, often measured in units like meters, kilometers, miles, etc. It can also refer to the extent of separation or remoteness between two things, whether it's geographical, spatial, or even conceptual.