Find the coordinates of B

Question

Find the coordinates of B when it is given that A(5,-2) and M(12,6), M is the midpoint in this problem. I keep getting (8.5,2) for the answer and I don't think that is correct. Can someone please explain it to me?

Answer 1

If M is the mid-point of line segment AB, and the coordinates of A = (5,-2) while the coordinates of B = (12,6), then the coordinates of M = (8.5,2), which is what you stated that you got.

 

However, that is not what was asked. You are provided with M = (12,6) so you need to identify the coordinates of B. So, just ask yourself how did I get from A to M ? The answer is move 7 right and 8 up since 5 + 7 = 12 while -2 + 8 = 6. All you have to do is add 7 more to the x-value and 8 more to the y-value to obtain the correct answer of (19,14).

Answer 2

Hi Jane, the midpoint on a line is given by the equation:

 

M = (A + B) / 2

 

M is: (12, 6)

 

A is: (5, -2)

 

B is: (x, y)

 

We need to find B

 

Substitute for A and M:

 

(12, 6) = ((5, -2) + (x, y)) / 2

 

Multiply both sides by 2:

 

(24, 12) = (5, -2) + (x, y)

 

Subtract (5, -2) from both sides:

 

(19, 14) = (x, y)

 

Point B is: (19, 14)

 

Check:

 

(12, 6) = ((5, -2) + (19, 14)) / 2

 

(12, 6) = (24, 12) / 2

 

(12, 6) = (12, 6), values check.

 

Questions?

Answer 3

(x of pt A + x of pt B)/2 =  mdpt x

(5 + x) / 2 = 12      multiply both sides by 2

5 + x = 24              subtract 5 from both sides

x = 19

 

(y of pt A + y of pt B)/2 = mdpt y

(-2 + y)/2 = 6        multiply both sides by 2

-2 + y = 12            add 2 to both sides

y = 14

 

B is (19,  14)