Question

Suppose line segment AB has one endpoint at A(0,0). If (5,3) is the midpoint of AB, what are the coordinates of point B?

a. (10,6)
b. (4,3)
c. (0,0)
d. (-5,-3)

Answer 1

To find point B's coordinates when (5,3) is the midpoint and A(0,0) is one endpoint, solve for x2 and y2 using the midpoint formula. The correct coordinates for B are (10,6).

Step-by-step explanation:

To find the coordinates of point B given that (5,3) is the midpoint of line segment AB, and A(0,0) is one endpoint, we use the midpoint formula: the midpoint M(x, y) = ((x1 + x2)/2, (y1 + y2)/2), where (x1, y1) and (x2, y2) are the coordinates of the endpoints A and B respectively.

Using the coordinates of A(0,0) and M(5,3), we can set up the following equations:

• x-coordinate: (0 + x2)/2 = 5
• y-coordinate: (0 + y2)/2 = 3

By solving these equations, we find that x2 = 10 and y2 = 6. Therefore, the coordinates of point B are (10,6).

The correct answer is a. (10,6).