Question

find the distance between the points a (-4,-3) and b (6,-2) by using the distance formula. leave your answer under the radical unless it is a perfect square. if you give a decimal answer, round to the nearest tenth. possible points: 1

Explanation:

Step1: Identify the distance - formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1=-4,y_1 = - 3,x_2=6,y_2=-2$.

Step2: Calculate the differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=6-(-4)=10$ and $y_2 - y_1=-2-(-3)=1$.

Step3: Substitute into the formula

Substitute the values into the distance formula: $d=\sqrt{(10)^2+(1)^2}=\sqrt{100 + 1}=\sqrt{101}$.

Answer:

$\sqrt{101}$