Question

Find the distance between the points 11,4 and 10,5

Answer 1

The distance between the points (11,4) and (10,5) is √(2), which is approximately 1.414 units, calculated using the distance formula derived from the Pythagorean theorem.

Step-by-step explanation:

To find the distance between the points (11,4) and (10,5), we can apply the distance formula, which is derived from the Pythagorean theorem.

The distance formula is √((x2-x1)² + (y2-y1)²), where (x1,y1) and (x2,y2) are the coordinates of the two points.

Plugging in the given coordinates, we have:

• x1 = 11, y1 = 4
• x2 = 10, y2 = 5

Distance = √((10 - 11)² + (5 - 4)²) = √((-1)² + (1)²) = √(1 + 1) = √(2)

The exact distance is √(2) units. To express √(2) as a decimal, it is approximately 1.414.

Therefore, the distance between the points (11,4) and (10,5) is approximately 1.414 units.

Answer 2

The distance between the points is
`√(2) \ units}`

Finding the distance between two points

The distance between points on a cartesian plane can be determined by using the distance formula. This distance clearly shows the varying distance between two points of a line segment on the cartesian plane.

From the information given;

Let x₁ = 11, and y₁ = 4

Let x₂ = 10 and y₂ = 5

Using the distance formula:

`d = \sqrt {(x_2-x_1)^2 + (y_2-y_1)^2 }}`

`d = \sqrt {(10-11)^2 + (5-4)^2 }}`

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

`d = \sqrt {1+1 }}`

`d = \sqrt {2 }\ units}`

Therefore, the distance between the two points is
`√(2)` units.