Chapter 0.1, Problem 1E

To determine

The coordinate increments $\Delta x$ and $\Delta y$ , from $A$ to $B$ .

Answer to Problem 1E

The values of $\Delta x=-2$ and $\Delta y=-3$ .

Explanation of Solution

Given:

  $A\left(1,2\right),B\left(-1,-1\right)$

Calculation:

Find the values of $\Delta x$ and $\Delta y$ :

The formula for $\Delta x$ change in $x-$ value:

  $\Delta x=\left(x-\text{value at point }B\right)-\left(x-\text{value at point }A\right)$

Substitute the values $x-$ value at point $B=-1$ and $x-$ value at point $A=1$ :

  $\begin{array}{l}\Delta x=-1-1\\ \Delta x=-2\end{array}$

The formula for $\Delta y$ change in $y-$ value:

  $\Delta y=\left(y-\text{value at point }B\right)-\left(y-\text{value at point }A\right)$

Substitute the values $y-$ value at point $B=-1$ and $y-$ value at point $A=2$ :

  $\begin{array}{l}\Delta y=-1-2\\ \Delta y=-3\end{array}$

Thus, the values of $\Delta x=-2$ and $\Delta y=-3$ .