Question

What are the coordinates of point B?

Enter your answer as an ordered pair, formatted like this: (42, 53)
AB has endpoints A and B, with point A at (6,5). AB has midpoint M at (4,6)__
What are the coordinates of point B?
Enter your answer as an ordered pair, formatted like this: (42, 53)'

Answer 1

Using the midpoint formula in reverse, we find the coordinates of point B are (2, 7), given the coordinates of point A (6,5) and midpoint M (4,6).

Step-by-step explanation:

To determine the coordinates of point B given the coordinates of point A (6,5) and the midpoint M (4,6), we can use the midpoint formula, which states that the midpoint M of a line segment with endpoints A (x1,y1) and B (x2,y2) is given by M = ((x1+x2)/2, (y1+y2)/2). Since we know the coordinates of A and M, we can solve for the coordinates of B.

Given:

A = (6,5)

M = (4,6)

We apply the midpoint formula in reverse to find B:

(4,6) = ((6+x2)/2, (5+y2)/2)

Now we solve for x2 and y2:

4 = (6+x2)/2

8 = 6 + x2

x2 = 8 - 6

x2 = 2

Solve for y2:

6 = (5+y2)/2

12 = 5 + y2

y2 = 12 - 5

y2 = 7

Therefore, the coordinates of point B are (2, 7).