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User TNguyen
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1 Answer

6 votes

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!

User Fceruti
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