Question

If the midpoint of line segment AB is M(6, -3) and the coordinates of point A are (4, -7), what are the coordinates of point B?

A) (8, 1)
B) (8, -1)
C) (10, -3)
D) (2, -5)

Answer 1

To find the coordinates of point B, we use the midpoint formula and solve for B's coordinates. After setting up the equations based on M(6, -3) and A(4, -7), we find that B is (8, 1), which matches option (A) (8, 1).

Step-by-step explanation:

To find the coordinates of point B given the midpoint M and one endpoint A of a line segment AB, we can use the midpoint formula which states that the coordinates of the midpoint M(x, y) are given by the average of the coordinates of A and B. That is:

M(x) = (A(x) + B(x)) / 2

M(y) = (A(y) + B(y)) / 2

Given M(6, -3) and A(4, -7), we can set up two equations:

6 = (4 + B(x)) / 2

-3 = (-7 + B(y)) / 2

Solving these equations gives us the coordinates of B:

B(x) = 2 * 6 - 4 = 8

B(y) = 2 * (-3) + 7 = 1

Therefore, the coordinates of point B are (8, 1), which corresponds to option A).