Question

1. find the distance between the two points, (-6,4) and (-1,8). state the answer in simplest radical form and state the answer as a decimal rounded to the nearest hundredth.

Explanation:

Step1: Identify the distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Assign values to variables

Let $(x_1,y_1)=(-6,4)$ and $(x_2,y_2)=(-1,8)$. Then $x_2 - x_1=-1-(-6)=5$ and $y_2 - y_1=8 - 4 = 4$.

Step3: Substitute into the formula

$d=\sqrt{(5)^2+(4)^2}=\sqrt{25 + 16}=\sqrt{41}$.

Step4: Calculate the decimal - form

Using a calculator, $\sqrt{41}\approx6.40$.

Answer:

Simplest radical form: $\sqrt{41}$
Decimal form: $6.40$