Question
The midpoint of line segment AB is (3.5,1). Point A is at (2,6). Where is point B located?
A. ( 9/4, 7/2)
B. (5, -4)
C. ( 5/2, 3/2)
D. (7, -3)
A. ( 9/4, 7/2)
B. (5, -4)
C. ( 5/2, 3/2)
D. (7, -3)
Answers
GPT 3.5
Let's denote the coordinates of point B as (x, y).
According to the midpoint formula, the x-coordinate of the midpoint is equal to the average of the x-coordinates of the two endpoints, and the y-coordinate of the midpoint is equal to the average of the y-coordinates of the two endpoints.
So, we have:
(2 + x)/2 = 3.5 (equation 1)
(6 + y)/2 = 1 (equation 2)
From equation 1, we can solve for x:
2 + x = 7
x = 7 - 2
x = 5
From equation 2, we can solve for y:
6 + y = 2
y = 2 - 6
y = -4
Therefore, point B is located at (5, -4).
Answer: B. (5, -4)
According to the midpoint formula, the x-coordinate of the midpoint is equal to the average of the x-coordinates of the two endpoints, and the y-coordinate of the midpoint is equal to the average of the y-coordinates of the two endpoints.
So, we have:
(2 + x)/2 = 3.5 (equation 1)
(6 + y)/2 = 1 (equation 2)
From equation 1, we can solve for x:
2 + x = 7
x = 7 - 2
x = 5
From equation 2, we can solve for y:
6 + y = 2
y = 2 - 6
y = -4
Therefore, point B is located at (5, -4).
Answer: B. (5, -4)