Question

The midpoint of AB is (6,5). If A(7,-10), find B:

A) B(5, 20)
B) B(6, 5)
C) B(7, 0)
D) B(8, 15)

Answer 1

To find point B when given the midpoint (6,5) and point A(7,-10), we use the midpoint formula, resulting in finding point B's coordinates to be (5, 20).

Step-by-step explanation:

The student asks to find point B given that the midpoint of line segment AB is (6,5), and point A is (7,-10). To find point B, we use the midpoint formula which is the average of the x-coordinates and the y-coordinates of points A and B respectively. Since we are given the midpoint, we can setup two equations to solve for B's coordinates.

Let B be (x,y). Thus, the midpoint M is calculated as:

• Mx = (Ax + x) / 2
• My = (Ay + y) / 2

Plugging in the known values for M, A, and the expressions for B:

• 6 = (7 + x) / 2
• 5 = (-10 + y) / 2

Solving these equations:

• 12 = 7 + x → x = 12 - 7 → x = 5
• 10 = -10 + y → y = 10 + 10 → y = 20

Therefore, the coordinates for point B are (5, 20), which corresponds to option A in the question provided by the student.