Find the distance for each segment.
X (3, 4) and Y (9, 4)
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.
please simplify the formula
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.
Find the distance for each segment. F (6, 0) and G (6, -11)
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.
Find the distance for each segment. (-10.5, -7.25) and D (18.5, -7.25)
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.
Find the distance for each segment. M (-1.3, -1.3) and N (-1.3, and 3.6)
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.
To find the distance between two points, X(3, 4) and Y(9, 4), you can use the distance formula, which is derived from the Pythagorean theorem.
The distance formula is:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this formula, (x1, y1) represents the coordinates of the first point (X in this case), and (x2, y2) represents the coordinates of the second point (Y in this case).
Let's calculate the distance between X(3, 4) and Y(9, 4):
d = sqrt((9 - 3)^2 + (4 - 4)^2)
= sqrt(6^2 + 0^2)
= sqrt(36 + 0)
= sqrt(36)
= 6
Therefore, the distance between X(3, 4) and Y(9, 4) is 6 units.