The coordinates of M, P and Q in terms of a and b are [tex]M = \frac{1}{2}\cdot a + \frac{1}{2}\cdot b[/tex], [tex]P = \frac{3}{4}\cdot a + \frac{1}{4}\cdot b[/tex] and [tex]Q = \frac{1}{8}\cdot a - \frac{1}{8}\cdot b[/tex], respectively.
In this question we are going to use definitions of vectors and product of a vector by a scalar. Based on the information given on statement, we have the following vectorial formulas:
Location of M
[tex]\overrightarrow{AM} = \frac{1}{2}\cdot \overrightarrow{AB}[/tex]
[tex]\vec M - \vec A = \frac{1}{2}\cdot \vec B - \frac{1}{2}\cdot \vec A[/tex]
[tex]\vec M = \frac{1}{2}\cdot \vec A +\frac{1}{2}\cdot \vec B[/tex]
[tex]M = \frac{1}{2}\cdot a + \frac{1}{2}\cdot b[/tex]
Location of P
[tex]\overrightarrow{AP} = \frac{1}{2}\cdot \overrightarrow{AM}[/tex]
[tex]\vec P - \vec A = \frac{1}{2}\cdot \vec M - \frac{1}{2}\cdot \vec A[/tex]
[tex]\vec P = \frac{1}{2}\cdot \vec A +\frac{1}{2}\cdot \vec M[/tex]
[tex]\vec P = \frac{3}{4}\cdot \vec A + \frac{1}{4}\cdot \vec B[/tex]
[tex]P = \frac{3}{4}\cdot a + \frac{1}{4}\cdot b[/tex]
Location of Q
[tex]\overrightarrow{QM} = \frac{1}{2}\cdot \overrightarrow{PM}[/tex]
[tex]\vec M - \vec Q = \frac{1}{2}\cdot \vec M - \frac{1}{2}\cdot \vec P[/tex]
[tex]\vec Q = \frac{1}{2}\cdot \vec P - \frac{1}{2}\cdot \vec M[/tex]
[tex]\vec Q = \frac{1}{2}\cdot \left(\frac{3}{4}\cdot \vec A + \frac{1}{4}\cdot \vec B\right) -\frac{1}{2}\cdot \left(\frac{1}{2}\cdot \vec A + \frac{1}{2}\cdot \vec B\right)[/tex]
[tex]\vec Q = \frac{1}{8}\cdot \vec A -\frac{1}{8}\cdot \vec B[/tex]
[tex]Q = \frac{1}{8}\cdot a - \frac{1}{8}\cdot b[/tex]
The coordinates of M, P and Q in terms of a and b are [tex]M = \frac{1}{2}\cdot a + \frac{1}{2}\cdot b[/tex], [tex]P = \frac{3}{4}\cdot a + \frac{1}{4}\cdot b[/tex] and [tex]Q = \frac{1}{8}\cdot a - \frac{1}{8}\cdot b[/tex], respectively.
We kindly invite to check this question on midpoints: https://brainly.com/question/4747771
