Chapter 1.1, Problem 4E

To determine

To find: The coordinate increments from $A\left(0,4\right)$ to $B\left(0,-2\right)$ .

Answer to Problem 4E

The coordinate increments from $A\left(0,4\right)$ to $B\left(0,-2\right)$ are $\Delta x=0$ and $\Delta y=-6$ .

Explanation of Solution

Given information: The initial point is $A\left(0,4\right)$ and the final point is $B\left(0,-2\right)$ .

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 $0$ for $x_2$ and $0$ for $x_1$ in the increment formula for $x$ -coordinate.

  $\begin{array}{c}\Delta x=x_2-x_1\\ =0-0\\ =0\end{array}$

So, the $x$ -coordinate increment from $A\left(0,4\right)$ to $B\left(0,-2\right)$ is $\Delta x=0$ .

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 $4$ for $y_1$ in the increment formula for $x$ -coordinate increment.

  $\begin{array}{c}\Delta y=y_2-y_1\\ =-2-4\\ =-6\end{array}$

So, the $y$ -coordinate increment from $A\left(0,4\right)$ to $B\left(0,-2\right)$ is $\Delta y=-6$ .

Therefore, the coordinate increments from $A\left(0,4\right)$ to $B\left(0,-2\right)$ are $\Delta x=0$ and $\Delta y=-6$ .