Geometry Question!!

[swimchamp101]

M is the midpoint of seg AB, Q is the midpoint of seg AM, and T is the midpoint of seg QM. If the coordinates of A and B are a and b, find the coordinates of Q and T in terms of a and b.

I'm pretty sure the answer is... Q 3a + b)/4; T: (5a + 3b)/8 but can someone give me a clear explanation as to why this is the answer and how to get to it.

 

[Mrspi]

M is the midpoint of seg AB, Q is the midpoint of seg AM, and T is the midpoint of seg QM. If the coordinates of A and B are a and b, find the coordinates of Q and T in terms of a and b.

I'm pretty sure the answer is... Q 3a + b)/4; T: (5a + 3b)/8 but can someone give me a clear explanation as to why this is the answer and how to get to it.

If A and B are points on a number line, with "a" being the coordinate of A and "b" being the coordinate of B, then the coordinate of M (the midpoint of AB) would be (a + b)/2

Now, Q is the midpoint of segment AM. To find the coordinate of Q, add the coordinates of A and Q, and multiply by 1/2:

the coordinate of Q is [a + (a + b)/2] * (1/2), or
[2a/2 + (a + b)/2] * (1/2), or
[(2a + a + b) / 2] * (1/2), or
(3a + b) / 2 * (1/2), or
(3a + b)/4

T is the midpoint of QM. So, the coordinate of T is found by adding the coordinates of Q and M, and multiply by 1/2.

The coordinate of T is [(3a + b)/4 + (a + b)/2] * (1/2)

See if you can simplify that expression!