A line segment has one endpoint at the coordinate (0, 1) and a midpoint at the coordinate (2, 4). Find the other endpoint.
a.)(1, 7)
b.)(4, 7)
c.)(1, 25)
I figured it out
(4,7)
Good job. :)
Given: (0,1), (2,4), (x,y).
x-0 = 2(2-0). X = 4.
y-1 = 2(4-1). Y = 7.
To find the other endpoint of a line segment, 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 given by the coordinates:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
In this case, we know that one endpoint has coordinates (0, 1), and the midpoint is (2, 4). Let's call the coordinates of the other endpoint (x, y).
Using the midpoint formula, we can set up the following equations:
((0 + x)/2, (1 + y)/2) = (2, 4)
Expanding these equations, we get:
(x/2, 1/2 + y/2) = (2, 4)
Now, equating the x and y coordinates separately, we have:
x/2 = 2 --> Multiply both sides by 2 to isolate x: x = 4
1/2 + y/2 = 4 --> Subtract 1/2 from both sides to isolate y/2: y/2 = 4 - 1/2 = 7/2
Multiply both sides by 2 to isolate y: y = 7
Therefore, the coordinates of the other endpoint are (4, 7).
So, the final answer is b.) (4, 7).