Question

What is the formula to calculate the distance between two points in a coordinate plane?

1) d = sqrt((x2 - x1)² + (y2 - y1)²)
2) d = (x2 - x1) + (y2 - y1)
3) d = sqrt((x2 - x1) + (y2 - y1))
4) = (x2 - x1)² + (y2 - y1)²

Answer 1

The formula to calculate the distance between two points in a coordinate plane is d = sqrt((x2 - x1)² + (y2 - y1)²). This formula uses the Pythagorean theorem to find the straight-line distance between two points.

Step-by-step explanation:

The formula to calculate the distance between two points in a coordinate plane is d = sqrt((x2 - x1)² + (y2 - y1)²).

This formula uses the Pythagorean theorem to find the straight-line distance between two points. It calculates the difference between the x-coordinates and the y-coordinates of the two points, squares them, sums them, and then takes the square root of the result.

For example, if the two points are (2, 3) and (5, 7), the formula would be:
d = sqrt((5 - 2)² + (7 - 3)²)
= sqrt(3² + 4²)
= sqrt(9 + 16)
= sqrt(25)
= 5