Question

Line segment AB lies in the standard coordinate plane. Point A is at (1,1). Point M, the midpoint of AB, is at (4,6). Which of the following could be the coordinates of point B?

A) (3.5, 4)
B) (5, 7)
C) (9, 13)
D) (25, 35)

Answer 1

The correct coordinates for point B are found by using the midpoint formula, resulting in point B being at (7,11), which corresponds to option C.

Step-by-step explanation:

The student wants to find the coordinates of point B given that point A is at (1,1), and point M, the midpoint of line segment AB, is at (4,6). To find B, we use the fact that the midpoint's coordinates are the average of the corresponding coordinates of A and B. Mathematically, we have the midpoint formula M = ((x1+x2)/2, (y1+y2)/2), where (x1, y1) are the coordinates of A and (x2, y2) are those of B.

We have A at (1,1) and M at (4,6). Therefore, we get the following equations:

• 4 = (1 + x2)/2
• 6 = (1 + y2)/2

Solving the first equation for x2, we multiply both sides by 2 to get 8 = 1 + x2, which simplifies to x2 = 7. Solving the second equation for y2, again we multiply both sides by 2 to get 12 = 1 + y2, which simplifies to y2 = 11.

Therefore, point B has the coordinates (7, 11), which makes option C, (7,11), the correct answer.