b is the midpoint of segment AC & its coordinate is 10. if segment BC=12, what are the coordinates of A and C?
To find the coordinates of A and C, we need to utilize the fact that B is the midpoint of segment AC.
Given that the coordinate of B is 10, we know that the average of the coordinates of A and C is equal to 10. This can be expressed mathematically as:
(x-coordinate of A + x-coordinate of C) / 2 = 10
Since B is the midpoint, the distance from A to B is the same as the distance from B to C. In this case, the distance from B to C is 12. This implies that the x-coordinate of C is 12 units greater than the x-coordinate of B. We can represent this as:
x-coordinate of C = x-coordinate of B + 12
Now we can solve for the coordinates of A and C.
1) Solving for the x-coordinate of A:
Substitute the given coordinate of B into the average equation:
(x-coordinate of A + 10) / 2 = 10
Multiply both sides of the equation by 2:
x-coordinate of A + 10 = 20
Subtract 10 from both sides of the equation:
x-coordinate of A = 10
Therefore, the x-coordinate of A is 10.
2) Solving for the x-coordinate of C:
Substitute the given coordinate of B into the equation for C:
x-coordinate of C = 10 + 12
Calculate:
x-coordinate of C = 22
Therefore, the x-coordinate of C is 22.
To summarize:
The coordinates of A are (10, y), where y can be any real number.
The coordinates of C are (22, y), where y can be any real number.