A line segment has end points of (4, -4) and
(0, 5). What are the coordinates of the midpoint of this line segment?
A) (2, 1/2)
B) (-2, -9/2)
C) (4, 1/2)
D) (8, -13)
the midpoint has the average coordinates of the ends:
( (4+0)/2 , (-4+5)/2 ) = (2,1/2)
Just to refresh your memory on why this is true,
the distance from a to b is b-a
the value halfway from a to b is thus
a + (b-a)/2 = (2a+b-a)/2 = (a+b)/2
Is the answer A then?
yes, but read what he said.
To find the midpoint of a line segment, you need to average the coordinates of the two endpoints.
Let's say the coordinates of the first endpoint are (x₁, y₁) = (4, -4), and the coordinates of the second endpoint are (x₂, y₂) = (0, 5).
To find the x-coordinate of the midpoint, you need to average the x-coordinates of the endpoints:
x-coordinate of midpoint = (x₁ + x₂) / 2 = (4 + 0) / 2 = 4/2 = 2.
To find the y-coordinate of the midpoint, you need to average the y-coordinates of the endpoints:
y-coordinate of midpoint = (y₁ + y₂) / 2 = (-4 + 5) / 2 = 1/2.
Therefore, the coordinates of the midpoint of the line segment are (2, 1/2).
So, the correct answer is A) (2, 1/2).