Question

What is the distance between point A and point B?
Point A (2,3)
Point B (5,9)

Answer 1

d ≈ 6.7 units

Step-by-step explanation:

calculate the distance, d, using the distance formula

d =
`\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2 }`

let (x₁, y₁ ) = A (2, 3 ) and (x₂, y₂ ) = B (5, 9 )

substitute these values into the formula for d

d =
`√((5-2)^2+(9-3)^2)`

=
`√(3^2+6^2)`

=
`√(9+36)`

=
`√(45)`

≈ 6.7 units ( to the nearest tenth )

Answer 2

The exact distance between point A(2,3) and point B(5,9) is √45 units, which approximately equals 6.71 units, representing the straight-line distance or magnitude of displacement in a two-dimensional plane.

Step-by-step explanation:

To calculate the distance between point A and point B with coordinates A(2,3) and B(5,9), we can use the distance formula derived from the Pythagorean theorem, which is the straight-line distance in a two-dimensional plane. The formula is:

d = √((x2 - x1)² + (y2 - y1)²)

Where:
(x1, y1) are the coordinates of point A, and
(x2, y2) are the coordinates of point B.

Substituting the given values, we get:

d = √((5 - 2)² + (9 - 3)²) = √(3² + 6²) = √(9 + 36) = √45

The exact distance is √45 units, or approximately 6.71 units if we calculate the square root. This is the straight-line distance or the magnitude of displacement from A to B. Such problems are common in vector addition and finding displacements in Cartesian planes.