Point J has coordinates 10 comma 8. The midpoint of the line segment J K is 6 comma 12.
What are the coordinates of point K ?
To find the coordinates of point K, we can use the midpoint formula, which states that the coordinates of the midpoint between two points (x1, y1) and (x2, y2) are ((x1+x2)/2, (y1+y2)/2).
Given that the midpoint of J and K is (6, 12) and J has coordinates (10, 8), we can set up the equation as follows:
((10 + x)/2, (8 + y)/2) = (6, 12)
Simplifying the equation, we get:
(10 + x)/2 = 6
8 + y)/2 = 12
Multiplying both sides of the first equation by 2, we have:
10 + x = 12
x = 12 - 10
x = 2
Multiplying both sides of the second equation by 2, we have:
8 + y = 24
y = 24 - 8
y = 16
Therefore, the coordinates of point K are (2, 16).
To find the coordinates of point K, we need to use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint of a line segment are given by the average of the coordinates of the endpoints.
Let's denote the coordinates of point K as (x, y).
Using the midpoint formula, we can set up the following equations:
x-coordinate: (10 + x)/2 = 6
y-coordinate: (8 + y)/2 = 12
Let's solve these equations to find the values of x and y:
For the x-coordinate:
(10 + x)/2 = 6
10 + x = 12
x = 12 - 10
x = 2
For the y-coordinate:
(8 + y)/2 = 12
8 + y = 24
y = 24 - 8
y = 16
Therefore, the coordinates of point K are (2, 16).