A line segment has an endpoint at (3,2). If the midpoint of the line segment is (6.-2), what are the coordinates of the point at the other end of the line segment?
please answer i need it by next class...
To find the coordinates of the other endpoint of the line segment, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points (x1, y1) and (x2, y2) are given by:
Midpoint: ((x1 + x2) / 2, (y1 + y2) / 2)
We are given the midpoint as (6, -2) and one endpoint as (3, 2). Let's call the coordinates of the other endpoint (x, y). We can set up the equation using the midpoint formula:
((3 + x) / 2, (2 + y) / 2) = (6, -2)
Now, let's solve for x and y:
(3 + x) / 2 = 6 --> 3 + x = 12 --> x = 9
(2 + y) / 2 = -2 --> 2 + y = -4 --> y = -6
Therefore, the coordinates of the point at the other end of the line segment are (9, -6).
To find the coordinates of the point at the other end of the line segment, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment can be found by taking the average of the x-coordinates and the average of the y-coordinates of the endpoints.
Let's call the coordinates of the other endpoint (x, y). Given that the midpoint of the line segment is (6, -2) and one endpoint is (3, 2), we can set up the following equations:
(x + 3) / 2 = 6 (for x-coordinates)
(y + 2) / 2 = -2 (for y-coordinates)
To solve for x, multiply both sides of the first equation by 2:
x + 3 = 12
Subtract 3 from both sides:
x = 9
So, the x-coordinate of the other endpoint is 9.
To solve for y, multiply both sides of the second equation by 2:
y + 2 = -4
Subtract 2 from both sides:
y = -6
Thus, the coordinates of the point at the other end of the line segment are (9, -6).
It's all a matter of knowing the basic distance and midpoint formulas.
The distance between two points with coordinates (x1,y1) and (x2,y2) is given by d=the square root of (x2-x1)^2 + (y2-y1)^2
If a line segment has endpoints at (x1,y1) and (x2,y2) the the midpoint of this line segment is found at (x1+x2/2, y1+y2/2)
In your case, you have two options. You can plug the two coordinates given into the distance formula and find the distance and then, plug (6,-2) and whatever distance you got before into it again to find the other point. Or you could plug all of the information you have into the midpoint formula and solve it out to find the other point.
Hope this helps!