Question

Calculate the distance between the points

G = (2,−2) and F = (9,−6) in the coordinate plane.

Give an exact answer (not a decimal approximation).

Answer 1

The distance between the points G = (2,-2) and F = (9,-6) in the coordinate plane is sqrt(65)

Step-by-step explanation:

To calculate the distance between two points in the coordinate plane, we can use the distance formula. The distance formula is:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Given the points G = (2, -2) and F = (9, -6), we can substitute these values into the formula:

d = sqrt((9 - 2)^2 + (-6 - (-2))^2)

d = sqrt(49 + 16)

d = sqrt(65)

Therefore, the distance between the points G and F is sqrt(65).