Find the coordinates of the midpoint of the segment whose endpoints are (-4, 6) and (-8, -2).
Well, since we're talking about a midpoint, it's like finding the middle ground between two places. It's like finding a compromise, you know? So, let's calculate the midpoint coordinates using a little math juggling!
To find the midpoint, we take the average of the x-coordinates and the average of the y-coordinates. So, let's do some math magic:
For the x-coordinate: (-4 + -8) / 2 = -12 / 2 = -6.
For the y-coordinate: (6 + -2) / 2 = 4 / 2 = 2.
Voila! The midpoint coordinates are (-6, 2), hidden right in the middle of all the mathematical hoopla!
To find the coordinates of the midpoint of a line segment, we can use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint (M) of a line segment with endpoints (x₁, y₁) and (x₂, y₂) are given by:
M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
In this case, the endpoints are (-4, 6) and (-8, -2). Let's substitute these values into the formula:
M = ((-4 + -8) / 2, (6 + -2) / 2)
Simplifying,
M = (-12 / 2, 4 / 2)
M = (-6, 2)
The coordinates of the midpoint of the segment are (-6, 2).
To find the coordinates of the midpoint of a segment, we need to average the x-coordinates and the y-coordinates of the endpoints.
To find the x-coordinate of the midpoint, we average the x-coordinates of the endpoints:
x-coordinate of midpoint = (x-coordinate of endpoint 1 + x-coordinate of endpoint 2) / 2
So, in this case:
x-coordinate of midpoint = (-4 + -8) / 2
To find the y-coordinate of the midpoint, we average the y-coordinates of the endpoints:
y-coordinate of midpoint = (y-coordinate of endpoint 1 + y-coordinate of endpoint 2) / 2
So, in this case:
y-coordinate of midpoint = (6 + -2) / 2
Now we can calculate the coordinates of the midpoint:
x-coordinate of midpoint = (-4 + -8) / 2 = -12 / 2 = -6
y-coordinate of midpoint = (6 + -2) / 2 = 4 / 2 = 2
Therefore, the coordinates of the midpoint of the segment are (-6, 2).
The mid-point between points P1(x1,y1) and P2(x2,y2) is
M((x1+x2)/2, (y1+y2)/2)