Question

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?

A) (2, 7)
B) (6, 6)
C) (4, 5)
D) (2, 5)

Answer 1

To find the coordinates of point B, use the midpoint formula to find the x-coordinate and y-coordinate of B. The coordinates of point B are (2, 7).

Step-by-step explanation:

To find the coordinates of point B, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint (M) between two points (A and B) is the average of the x-coordinates and the average of the y-coordinates:

Midpoint formula:

M = ((x1 + x2) / 2, (y1 + y2) / 2)

Given that point A has coordinates (6, 5) and the midpoint M has coordinates (4, 6), we can substitute these values into the formula:

4 = ((6 + x2) / 2)

Simplifying the equation, we can multiply both sides by 2:

8 = 6 + x2

Then, subtract 6 from both sides:

2 = x2

So the x-coordinate of point B is 2. Similarly, we can find the y-coordinate of point B:

6 = ((5 + y2) / 2)

Again, multiplying both sides by 2:

12 = 5 + y2

Subtracting 5 from both sides:

7 = y2

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