Chapter 1.1, Problem 2E

To determine

To find: The coordinate increments from $A\left(-3,2\right)$ to $B\left(-1,-2\right)$ .

Answer to Problem 2E

The coordinate increments from $A\left(-3,2\right)$ to $B\left(-1,-2\right)$ are $\Delta x=2$ and $\Delta y=-4$ .

Explanation of Solution

Given information: The initial point is $A\left(-3,2\right)$ and the final point is $B\left(-1,-2\right)$ .

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 $-1$ for $x_2$ and $-3$ for $x_1$ in the increment formula for $x$ -coordinate increment.

  $\begin{array}{c}\Delta x=x_2-x_1\\ =-1-\left(-3\right)\\ =-1+3\\ =2\end{array}$

So, the $x$ -coordinate increment from $A\left(-3,2\right)$ to $B\left(-1,-2\right)$ is $\Delta x=2$ .

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 $-2$ for $y_2$ and $2$ for $y_1$ in the increment formula for $y$ -coordinate increment.

  $\begin{array}{c}\Delta y=y_2-y_1\\ =-2-2\\ =-4\end{array}$

So, the $y$ -coordinate increment from $A\left(-3,2\right)$ to $B\left(-1,-2\right)$ is $\Delta y=-4$ .

Therefore, the coordinate increments from $A\left(-3,2\right)$ to $B\left(-1,-2\right)$ are $\Delta x=2$ and $\Delta y=-4$ .