Question

What is the length of a line segment on the coordinate plane with end point (3,5) and (6,8) to the nearest tenth

Answer 1

4.24 units

Explanation:

We can use the distance formula to solve this.

Distance formula: d = √((x₁ - x₂)² + (y₁ - y₂)²), where (x₁, y₁) and (x₂, y₂) are the two coordinates.

Plug in: d = √((3 - 6)² + (5 - 8)²)

Subtract: d = √((-3)² + (-3)²))

Square: d = √(9 + 9)

Add: d = √18

Square root: d = 4.24264... ≈ 4.24 units

Answer 2

Explanation:

Use the distance formula for coordinate geoemetry and the fact that x1 = 3, y1 = 5, x2 = 6 and y2 = 8 to fill in the formula:

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

fills in accordingly:

`d=√((6-3)^2+(8-5)^2)`

which simplifies a bit to

`d=√((3)^2+(3)^2)`

which is

`d=√(18)`

The square root of 18 simplifies down to
`3√(2)`, which is 4.2426 in decimal form