Chapter 13.4, Problem 29WE

a.

To determine

To calculate: Vector $\overrightarrow{AB}$ and $\overrightarrow{AM}$ and $\overrightarrow{AT}$ .

Answer to Problem 29WE

Vector $\overrightarrow{AB}=\left(18,18\right)$ , $\overrightarrow{AM}=\left(9,9\right)$ , $\overrightarrow{AT}=\left(6,6\right)$ .

Explanation of Solution

Given information: In the diagram, M is the mid-point of $\overrightarrow{AB}$ and T is a trisector point of $\overrightarrow{AB}$ .

  

In the diagram, M is the mid-point of $\overrightarrow{AB}$

Vector

  $\begin{array}{l}\overrightarrow{AB}=\left(20-2,21-3\right)\\ \overrightarrow{AB}=\left(18,18\right)\end{array}$

M is the mid-point of $\overrightarrow{AB}$

Then

  $M=\left(11,12\right)$

Vector $\overrightarrow{AM}$

  $\begin{array}{l}\overrightarrow{AM}=\left(11-2,12-3\right)\\ \overrightarrow{AM}=\left(9,9\right)\end{array}$

Trisector means dividing a line segment in the ratio $1:2$ and $2:1$

  $\begin{array}{l}T=\left(\frac{1\times 20+2\times 2}{3},\frac{1\times 21+2\times 3}{3}\right)\\ T=\left(8,9\right)\end{array}$

Vector $\overrightarrow{AT}$

  $\begin{array}{l}\overrightarrow{AT}=\left(8-2,9-3\right)\\ \overrightarrow{AT}=\left(6,6\right)\end{array}$

b.

To determine

To find: The co-ordinates of M and T .

Answer to Problem 29WE

M is the mid-point of $\overrightarrow{AB}$

Then

  $M=\left(11,12\right)$

The co-ordinates of $T=\left(8,9\right)$ .

Explanation of Solution

Given information: In the diagram, M is the mid-point of $\overrightarrow{AB}$ and T is a trisector point of $\overrightarrow{AB}$ .

  

In the diagram, M is the mid-point of $\overrightarrow{AB}$

Vector

  $\begin{array}{l}\overrightarrow{AB}=\left(20-2,21-3\right)\\ \overrightarrow{AB}=\left(18,18\right)\end{array}$

M is the mid-point of $\overrightarrow{AB}$

Then

  $M=\left(11,12\right)$

Trisector means dividing a line segment in the ratio $1:2$ and $2:1$

  $\begin{array}{l}T=\left(\frac{1\times 20+2\times 2}{3},\frac{1\times 21+2\times 3}{3}\right)\\ T=\left(8,9\right)\end{array}$