Question

Find the distance for each segment.
X (3, 4) and Y (9, 4)

Answer 1

please simplify the formula

Answer 2

Find the distance for each segment. F (6, 0) and G (6, -11)

Answer 3

Find the distance for each segment. (-10.5, -7.25) and D (18.5, -7.25)

Answer 4

Find the distance for each segment. M (-1.3, -1.3) and N (-1.3, and 3.6)

Answer 5

The distance for the segment XY can be found using the distance formula:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Substituting the coordinates of X and Y:

d = √[(9 - 3)² + (4 - 4)²]
d = √[6² + 0²]
d = √36
d = 6

Therefore, the distance for the segment XY is 6 units.

Answer 6

The distance formula is:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

This formula represents the distance between two points (x₁, y₁) and (x₂, y₂) in a two-dimensional plane.

To simplify it, we can break it down into smaller steps.

Step 1: Subtract the x-coordinates

(x₂ - x₁)

This gives us the horizontal distance between the points.

Step 2: Square the result of Step 1

(x₂ - x₁)²

This gives us the square of the horizontal distance.

Step 3: Subtract the y-coordinates

(y₂ - y₁)

This gives us the vertical distance between the points.

Step 4: Square the result of Step 3

(y₂ - y₁)²

This gives us the square of the vertical distance.

Step 5: Add the results of Step 2 and Step 4

(x₂ - x₁)² + (y₂ - y₁)²

This gives us the sum of the squares of the horizontal and vertical distances.

Step 6: Take the square root of the result of Step 5

√[(x₂ - x₁)² + (y₂ - y₁)²]

This gives us the actual distance between the two points.

So, the distance formula is a way of calculating the distance between two points based on their coordinates.

Answer 7

The distance for the segment FG can be found using the distance formula:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Substituting the coordinates of F and G:

d = √[(6 - 6)² + (-11 - 0)²]
d = √[0² + (-11)²]
d = √121
d = 11

Therefore, the distance for the segment FG is 11 units.

Answer 8

The distance for the segment between (-10.5, -7.25) and D (18.5, -7.25) can be found using the distance formula:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Substituting the coordinates, we get:

d = √[(18.5 - (-10.5))² + (-7.25 - (-7.25))²]
d = √[29² + 0²]
d = √841
d = 29

Therefore, the distance for the segment between (-10.5, -7.25) and D (18.5, -7.25) is 29 units.

Answer 9

The distance for the segment MN can be found using the distance formula:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Substituting the coordinates of M and N:

d = √[(-1.3 - (-1.3))² + (3.6 - (-1.3))²]
d = √[0² + 4.9²]
d = √24.01
d = 4.9

Therefore, the distance for the segment MN is 4.9 units.