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Chapter 2: Q21 (page 47)

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

Short Answer

Expert verified

Coordinates of Q is 3a+b4 andTis5a+3b8

Step by step solution

01

Step 1. State the definition of midpoint.

A midpoint is a point on a line segment that divides it into equal segments.

Here, M is the midpoint of AB炉, Q is the midpoint of AM炉, and T is the midpoint of QM炉and the coordinates of A and B are a and b respectively.

02

Step 2. Calculate the coordinate of Q.

As M is the midpoint of AB炉,

Then, the coordinate of AM is a+b2.

It is also given that Q is the midpoint of AM炉,

Then, the coordinate of Q is:

a+a+b22=2a+a+b22=3a+b4

03

Step 3. Calculate the coordinate of T.

As T is the midpoint of QM炉,

Then, the coordinate of T is:

a+b2+3a+b42=2a+2b+3a+b42

=2a+2b+3a+b8

=5a+3b8

04

Step 4. State the conclusion.

Therefore, the coordinate of Q is 3a+b4 and the coordinate of T is 5a+3b8.

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