the midpoint of line segment XY is at (2, 8) and point X is at (10, 4), what is the ordered pair of point Y?
To find the ordered pair of point Y, we need to determine the coordinates of point Y.
Given that the midpoint of line segment XY is (2, 8), we can use the midpoint formula to find the coordinates of Y.
The midpoint formula is:
Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
Let's substitute the given values into the formula:
(2, 8) = [(10 + x)/2, (4 + y)/2]
To simplify, let's solve for x and y separately.
For x:
2 = (10 + x)/2
2 * 2 = 10 + x
4 = 10 + x
x = 4 - 10
x = -6
For y:
8 = (4 + y)/2
8 * 2 = 4 + y
16 = 4 + y
y = 16 - 4
y = 12
Therefore, the ordered pair of point Y is (-6, 12).
To find the ordered pair of point Y, we'll use the formula for finding the midpoint of a line segment. The midpoint is the average of the x-coordinates and the average of the y-coordinates of the two endpoints.
Let's denote the coordinates of point Y as (x, y).
The midpoint coordinates are given as (2, 8), and the coordinates of point X are given as (10, 4).
To find the x-coordinate of point Y, we'll compute the average of the x-coordinates of the endpoints:
(x + 10) ÷ 2 = 2
Simplifying this equation, we have:
x + 10 = 4
Now, subtracting 10 from both sides, we find:
x = -6
To find the y-coordinate of point Y, we'll compute the average of the y-coordinates of the endpoints:
(y + 4) ÷ 2 = 8
Simplifying this equation, we have:
y + 4 = 16
Now, subtracting 4 from both sides, we find:
y = 12
Therefore, the ordered pair of point Y is (-6, 12).
To find the ordered pair of point Y, we need to use the midpoint formula. The midpoint formula states that the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is given by the coordinates ((x₁ + x₂)/2, (y₁ + y₂)/2).
In this case, we are given the coordinates of the midpoint (2, 8) and one endpoint X is (10, 4). Let's assume the coordinates of point Y are (x, y).
Using the midpoint formula, we can set up the following equations:
((10 + x)/2, (4 + y)/2) = (2, 8)
Since the x-coordinate of the midpoint is the average of the x-coordinates of the endpoints, we can equate the x-coordinates:
(10 + x)/2 = 2
To solve for x, we can multiply both sides by 2:
10 + x = 4
x = 4 - 10
x = -6
Now let's solve for y. Since the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints, we can equate the y-coordinates:
(4 + y)/2 = 8
To solve for y, we can multiply both sides by 2:
4 + y = 16
y = 16 - 4
y = 12
Therefore, the ordered pair of point Y is (-6, 12).