Question

Rachel starts on the grid at (-4,-5). She starts to walk and after an hour she is at the point (-3,-1). If shecontinues to walk at the same rate in the exact same direction for another hour, what will be the point whereshe stops?

Answer 1

(-2, 3)

Step-by-step explanation

Rachel starts at (-4, -5) and walks all the way to (-3, -1) in one hour.

We want to find her position if she continues at the same rate for another hour.

What we can do to find this position is to first find the slope of the line that connects her starting point and current point in fraction form.

That is:

`\begin{gathered} \text{slope = }(y_2-y_1)/(x_2-x_1) \\ \text{slope = }\frac{-1\text{ - (-5)}}{-3\text{ -(-4)}}\text{ = }\frac{-1\text{+ 5}}{-3\text{ + 4}} \\ \text{slope = }(4)/(1) \end{gathered}`

We are going to leave it as a fraction purposely.

The numerator is the change in y while the denominator is the change in x.

This means that the change in one hour occurs by adding 4 to the y cordinate and adding 1 to the x cordinate.

Therefore, after another hour, her new cordinate will be:

(-3 + 1, -1 + 4)

=> (-2, 3)

That is the position that she will stop.