How do I find the coordinates of the endpoint of a line if I already know the coordinates of the midpoint and the coordinates of the other endpoint?
To find the coordinates of the endpoint of a line, given the coordinates of the midpoint and the coordinates of the other endpoint, follow these steps:
1. Write down the coordinates of the midpoint. Let's say it is (x1, y1).
2. Write down the coordinates of the other endpoint. Let's say it is (x2, y2).
3. Use the midpoint formula to find the x-coordinate of the endpoint:
x = 2 * x1 - x2
4. Use the midpoint formula to find the y-coordinate of the endpoint:
y = 2 * y1 - y2
5. The coordinates of the endpoint of the line are (x, y).
By using the midpoint formula, you can determine the mirror image of the other endpoint across the midpoint, giving you the coordinates of the missing endpoint.
To find the coordinates of the endpoint of a line if you already know the coordinates of the midpoint and the coordinates of the other endpoint, you can use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint between two points (x₁, y₁) and (x₂, y₂) can be found by taking the average of the x-coordinates ( (x₁ + x₂)/2 ) and the average of the y-coordinates ( (y₁ + y₂)/2 ).
Let's say you have the coordinates of the midpoint (M) as (xₘ, yₘ) and the coordinates of the known endpoint (A) as (x₁, y₁). And you want to find the coordinates of the unknown endpoint (B). The coordinates of B can be calculated using the following steps:
1. Calculate the difference between the coordinates of the midpoint and the known endpoint:
Δx = xₘ - x₁
Δy = yₘ - y₁
2. Add the respective differences to the coordinates of the midpoint to get the coordinates of the unknown endpoint:
x₂ = xₘ + Δx (x-coordinate of B)
y₂ = yₘ + Δy (y-coordinate of B)
So, by applying the above steps, you can find the coordinates of the endpoint B based on the coordinates of the midpoint M and the known endpoint A using the midpoint formula and simple algebraic manipulations.
To find the coordinates of the endpoint of a line given the coordinates of the midpoint and the coordinates of the other endpoint, you can use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) are given by the following formulas:
x-coordinate of the midpoint = (x1 + x2) / 2
y-coordinate of the midpoint = (y1 + y2) / 2
Given the coordinates of the midpoint (x_mid, y_mid) and the coordinates of one endpoint (x_end, y_end), you can use the midpoint formula to find the coordinates of the other endpoint. Here are the steps:
1. Subtract the x-coordinate of the midpoint (x_mid) from the double of the x-coordinate of the endpoint (x_end) to get the x-coordinate of the other endpoint.
x_other_end = 2 * x_end - x_mid
2. Subtract the y-coordinate of the midpoint (y_mid) from the double of the y-coordinate of the endpoint (y_end) to get the y-coordinate of the other endpoint.
y_other_end = 2 * y_end - y_mid
So, the coordinates of the other endpoint of the line are (x_other_end, y_other_end).