Question

Two points in the xy plane have Cartesian coordinates (6.50, −6.50) m and (−3.50, 3.50) m.

(a) Determine the distance between these points.

Answer 1

To determine the distance between two points with Cartesian coordinates (6.50, -6.50) m and (-3.50, 3.50) m, use the distance formula resulting in a distance of √2 times 10 meters.

Step-by-step explanation:

The question asks to determine the distance between two points with given Cartesian coordinates in the xy plane. The coordinates are (6.50, −6.50) m and (−3.50, 3.50) m. To calculate the distance between two points in a Cartesian plane, we use the distance formula:

D = √[(x2 - x1)² + (y2 - y1)²]

Applying the values from the points, we have:

D = √[(−3.50 - 6.50)² + (3.50 - (−6.50))²]

D = √[(-10)² + (10)²]

D = √[100 + 100]

D = √[200]

D = √[(2)(100)]

D = √2 × 10

D = √2 × 10 m

Hence, the distance between the two coordinates is √2 times 10 meters.