Answer:
1) Kansas
2) X = 2
3) Y = 6
Explanation:
1) To determine the state where you would find yourself at the halfway point between Fairfield, California (-10, 1), and Montgomery, Alabama (5, -3), we need to find the coordinates of the halfway point.
The coordinates of the halfway point can be found by taking the average of the x-coordinates and the average of the y-coordinates.
Average x-coordinate = (-10 + 5) / 2 = -5/2 = -2.5
Average y-coordinate = (1 + (-3)) / 2 = -2 / 2 = -1
Therefore, the coordinates of the halfway point are approximately (-2.5, -1).
Using these coordinates, we can determine the state by referring to a map.
Based on the approximate coordinates, the halfway point falls within the state of Kansas.
2) To find the x-coordinate of the endpoint of the line segment with one endpoint at (10, 12) and a midpoint at (6, 9), we can use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint between two points (x₁, y₁) and (x₂, y₂) are given by:
Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
We are given the coordinates of the midpoint (6, 9) and one endpoint (10, 12). Let's denote the x-coordinate of the other endpoint as x.
Using the midpoint formula, we can set up the following equation:
((10 + x) / 2, (12 + y) / 2) = (6, 9)
To find the x-coordinate of the endpoint, we can equate the x-values:
(10 + x) / 2 = 6
Simplifying the equation:
10 + x = 12
x = 12 - 10
x = 2
Therefore, the x-coordinate of the endpoint of the line segment is 2.
3) To find the y-coordinate of the endpoint of the line segment with one endpoint at (10, 12) and a midpoint at (6, 9), we can use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint between two points (x₁, y₁) and (x₂, y₂) are given by:
Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
We are given the coordinates of the midpoint (6, 9) and one endpoint (10, 12). Let's denote the y-coordinate of the other endpoint as y.
Using the midpoint formula, we can set up the following equation:
((10 + x) / 2, (12 + y) / 2) = (6, 9)
To find the y-coordinate of the endpoint, we can equate the y-values:
(12 + y) / 2 = 9
Simplifying the equation:
12 + y = 18
y = 18 - 12
y = 6
Therefore, the y-coordinate of the endpoint of the line segment is 6.
Hope this helps!