Chapter 1.1, Problem 3E

To determine

To find: The coordinate increments from $A\left(-3,1\right)$ to $B\left(-8,1\right)$ .

Answer to Problem 3E

The coordinate increments from $A\left(-3,1\right)$ to $B\left(-8,1\right)$ are $\Delta x=-5$ and $\Delta y=0$ .

Explanation of Solution

Given information: The initial point is $A\left(-3,1\right)$ and the final point is $B\left(-8,1\right)$ .

Calculation:

The $x$ -coordinate increment from $A\left(x_1,y_1\right)$ to $B\left(x_2,y_2\right)$ is $\Delta x=x_2-x_1$ .

Substitute $-8$ for $x_2$ and $-3$ for $x_1$ in the increment formula for $x$ -coordinate increment.

  $\begin{array}{c}\Delta x=x_2-x_1\\ =-8-\left(-3\right)\\ =-8+3\\ =-5\end{array}$

So, the $x$ -coordinate increment from $A\left(-3,1\right)$ to $B\left(-8,1\right)$ is $\Delta x=-5$ .

The $y$ -coordinate increment from $A\left(x_1,y_1\right)$ to $B\left(x_2,y_2\right)$ is $\Delta y=y_2-y_1$ .

Substitute $1$ for $y_2$ and $1$ for $y_1$ in the increment formula for $x$ -coordinate increment.

  $\begin{array}{c}\Delta y=y_2-y_1\\ =1-1\\ =0\end{array}$

So, the $y$ -coordinate increment from $A\left(-3,1\right)$ to $B\left(-8,1\right)$ is $\Delta y=0$ .

Therefore, the coordinate increments from $A\left(-3,1\right)$ to $B\left(-8,1\right)$ are $\Delta x=-5$ and $\Delta y=0$ .