Chapter 2: Q21 (page 47)

M is the midpoint of $\bar{A B}$ , Q is the midpoint of $\bar{A M}$ , and T is the midpoint of $\bar{Q M}$ . 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 $\frac{3 a + b}{4}$ andTis $\frac{5 a + 3 b}{8}$

Step by step solution

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 $\bar{A B}$ , Q is the midpoint of $\bar{A M}$ , and T is the midpoint of $\bar{Q M}$ and the coordinates of A and B are a and b respectively.

Step 2. Calculate the coordinate of Q.

As M is the midpoint of $\bar{A B}$ ,

Then, the coordinate of AM is $\frac{a + b}{2}$ .

It is also given that Q is the midpoint of $\bar{A M}$ ,

Then, the coordinate of Q is:

$\begin{matrix} \frac{a + \frac{a + b}{2}}{2} = \frac{\frac{2 a + a + b}{2}}{2} \\ = \frac{3 a + b}{4} \end{matrix}$

Step 3. Calculate the coordinate of T.

As T is the midpoint of $\bar{Q M}$ ,

Then, the coordinate of T is:

$\frac{\frac{a + b}{2} + \frac{3 a + b}{4}}{2} = \frac{\frac{2 a + 2 b + 3 a + b}{4}}{2}$

$= \frac{2 a + 2 b + 3 a + b}{8}$

$= \frac{5 a + 3 b}{8}$

Step 4. State the conclusion.

Therefore, the coordinate of Q is $\frac{3 a + b}{4}$ and the coordinate of T is $\frac{5 a + 3 b}{8}$ .

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M is the midpoint of $\bar{A B}$ , Q is the midpoint of $\bar{A M}$ , and T is the midpoint of $\bar{Q M}$ . 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

Step by step solution

Step 1. State the definition of midpoint.

Step 2. Calculate the coordinate of Q.

Step 3. Calculate the coordinate of T.

Step 4. State the conclusion.

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M is the midpoint of AB¯, Q is the midpoint of AM¯, and T is the midpoint of 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.

Short Answer

Step by step solution

Step 1. State the definition of midpoint.

Step 2. Calculate the coordinate of Q.

Step 3. Calculate the coordinate of T.

Step 4. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

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M is the midpoint of $\bar{A B}$ , Q is the midpoint of $\bar{A M}$ , and T is the midpoint of $\bar{Q M}$ . If the coordinates of A and B are a and b, find the coordinates of Q and T in terms of a and b.