the end point of a line segment is (-3,7) and the midpoint is (1-1) find the other endpoint
since the midpoint is halfway from one end to the other,
-3 to 1 is 4, so add 4 more: 5
7 to -1 is -8, so subtract another 8: -9
the other end is (5,-9)
check: (-3+5)/2 = 1
(7-9)/2 = -1
To find the other endpoint of the line segment, we can use the formula for the midpoint of a line segment.
The midpoint formula states that the coordinates of the midpoint between two endpoints, (x₁, y₁) and (x₂, y₂), are the averages of their respective coordinates. So, we can set up the following equations:
Midpoint formula for x-coordinate:
(x₁ + x₂)/2 = x-midpoint
Midpoint formula for y-coordinate:
(y₁ + y₂)/2 = y-midpoint
Plugging in the given values:
(x₁ + x₂)/2 = 1
(-3 + x₂)/2 = 1
Simplifying the equations:
(x₂ - 3)/2 = 1
Now, we can solve for x₂:
(x₂ - 3) = 2 * 1
x₂ - 3 = 2
x₂ = 2 + 3
x₂ = 5
So, the x-coordinate for the other endpoint is 5.
Using the same logic, we can write the equation for the y-coordinate:
(y₁ + y₂)/2 = -1
(7 + y₂)/2 = -1
Simplifying the equation:
(7 + y₂) = 2 * -1
7 + y₂ = -2
y₂ = -2 - 7
y₂ = -9
Therefore, the y-coordinate for the other endpoint is -9.
Hence, the other endpoint of the line segment is (5, -9).