Final answer:
To find the distance between the points (9,1) and (6,-4), the distance formula is used, resulting in approximately 5.83 units. Distance is a scalar quantity, only representing magnitude without direction.
Step-by-step explanation:
The question asks us to find the distance between two points on the Cartesian plane. These points are (9,1) and (6,-4). To calculate the distance between two points, we can use the distance formula derived from the Pythagorean theorem. The formula is:
d = √((x2 - x1)² + (y2 - y1)²)
Applying the formula to our points:
d = √((6 - 9)² + (-4 - 1)²)
d = √((-3)² + (-5)²)
d = √(9 + 25)
d = √34
d ≈ 5.83 units
The distance between the points (9,1) and (6,-4) is approximately 5.83 units. It is important to remember that distance is a scalar quantity, which means it has only magnitude and no direction.