Question

Two points in the xy plane have Cartesian coordinates (2.50,−3.50}m and (−5.00,5.00)m.

(a) Determine the distance between these points.

Answer 1

The distance between the two points is 11.34 meters.

Step-by-step explanation:

To find the distance between two points in the Cartesian plane, we can use the distance formula:

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

Using the coordinates (2.50, -3.50) for point A and (-5.00, 5.00) for point B, we have:

d = sqrt((-5.00 - 2.50)^2 + (5.00 - (-3.50))^2)

Simplifying the equation gives us:

d = sqrt((-7.50)^2 + (8.50)^2)

Calculating the square root of the sum of the squares gives us the final distance:

d = sqrt(56.25 + 72.25)

d = sqrt(128.50)

d = 11.34 meters (rounded to two decimal places).