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My name is Ann [436]
2 years ago
12

Suppose M is the midpoint of Segment AB, P is the midpoint of Segment AM, and Q is the midpoint of segment PM.

Mathematics
1 answer:
DerKrebs [107]2 years ago
4 0

The coordinates of M, P and Q in terms of a and b are M = \frac{1}{2}\cdot a + \frac{1}{2}\cdot b, P = \frac{3}{4}\cdot a + \frac{1}{4}\cdot b and Q = \frac{1}{8}\cdot a - \frac{1}{8}\cdot b, 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

\overrightarrow{AM} = \frac{1}{2}\cdot \overrightarrow{AB}

\vec M - \vec A = \frac{1}{2}\cdot \vec B - \frac{1}{2}\cdot \vec A

\vec M = \frac{1}{2}\cdot \vec A +\frac{1}{2}\cdot \vec B

M = \frac{1}{2}\cdot a + \frac{1}{2}\cdot b

Location of P

\overrightarrow{AP} = \frac{1}{2}\cdot \overrightarrow{AM}

\vec P - \vec A = \frac{1}{2}\cdot \vec M - \frac{1}{2}\cdot \vec A

\vec P = \frac{1}{2}\cdot \vec A +\frac{1}{2}\cdot \vec M

\vec P = \frac{3}{4}\cdot \vec A  + \frac{1}{4}\cdot \vec B

P = \frac{3}{4}\cdot a + \frac{1}{4}\cdot b

Location of Q

\overrightarrow{QM} = \frac{1}{2}\cdot \overrightarrow{PM}

\vec M - \vec Q = \frac{1}{2}\cdot \vec M - \frac{1}{2}\cdot \vec P

\vec Q = \frac{1}{2}\cdot \vec P - \frac{1}{2}\cdot \vec M

\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)

\vec Q = \frac{1}{8}\cdot \vec A -\frac{1}{8}\cdot \vec B

Q = \frac{1}{8}\cdot a - \frac{1}{8}\cdot b

The coordinates of M, P and Q in terms of a and b are M = \frac{1}{2}\cdot a + \frac{1}{2}\cdot b, P = \frac{3}{4}\cdot a + \frac{1}{4}\cdot b and Q = \frac{1}{8}\cdot a - \frac{1}{8}\cdot b, respectively.

We kindly invite to check this question on midpoints: brainly.com/question/4747771

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