The midpoint of segment XY is (6, -3). The coordinates of one endpoint are X(-1, 8). Find the coordinates of endpoint Y.
(6,-3) is halfway from (-1,8) to Y
6-(-1) = 7
so, add 7 to 6 and get 13.
So, the x-coordinate of Y is 13
-1..........6..........13
6 is halfway from -1 to 13
(x+(-1))/2 = 6
x-1 = 12
x = 13
now do the same for y.
Well, let's figure this out. Since the midpoint of segment XY is given as (6, -3), we know that the average of the x-coordinates and the average of the y-coordinates of the two endpoints should give us those values.
So, let's start with the x-coordinate. The average of -1 and the x-coordinate of Y should give us 6. To find the other endpoint's x-coordinate, we can simply apply basic arithmetic:
(-1 + x-coordinate of Y)/2 = 6
-1 + x-coordinate of Y = 12
x-coordinate of Y = 13
For the y-coordinate, we can do the same thing. The average of 8 and the y-coordinate of Y should give us -3:
(8 + y-coordinate of Y)/2 = -3
8 + y-coordinate of Y = -6
y-coordinate of Y = -14
So, the coordinates of endpoint Y are (13, -14). Voila!
To find the coordinates of endpoint Y, we can use the midpoint formula. The midpoint formula states that the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is the coordinates ((x1 + x2) / 2, (y1 + y2) / 2).
Given that the midpoint of segment XY is (6, -3) and one endpoint is X(-1, 8), we can substitute these values into the midpoint formula:
(6, -3) = ((-1 + x2) / 2, (8 + y2) / 2)
Simplifying the formula, we can write:
6 = (-1 + x2) / 2
-3 = (8 + y2) / 2
To solve for x2, we can multiply both sides of the first equation by 2:
12 = -1 + x2
x2 = 12 + 1
x2 = 13
To solve for y2, we can also multiply both sides of the second equation by 2:
-6 = 8 + y2
y2 = -6 - 8
y2 = -14
Therefore, the coordinates of endpoint Y are Y(13, -14).
To find the coordinates of endpoint Y, you can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points (x₁, y₁) and (x₂, y₂) is:
((x₁ + x₂)/2, (y₁ + y₂)/2)
Given that the midpoint of segment XY is (6, -3) and one endpoint, X, is (-1, 8), you can plug these values into the midpoint formula and solve for the coordinates of endpoint Y.
Let's substitute the known values into the midpoint formula:
(6, -3) = ((-1 + x₂)/2, (8 + y₂)/2)
Now, we can simplify the equation:
6 = (-1 + x₂)/2
-3 = (8 + y₂)/2
To solve for x₂, multiply both sides of the first equation by 2:
12 = -1 + x₂
Adding 1 to both sides, we get:
13 = x₂
To solve for y₂, multiply both sides of the second equation by 2:
-6 = 8 + y₂
Subtracting 8 from both sides, we get:
-14 = y₂
Therefore, the coordinates of endpoint Y are (13, -14).