Question

find the distance between the points a (2,3) and b (5,8) 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.

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, $x_1 = 2,y_1 = 3,x_2 = 5,y_2 = 8$.

Step2: Calculate the differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=5 - 2=3$ and $y_2 - y_1=8 - 3 = 5$.

Step3: Square the differences and sum them

$(x_2 - x_1)^2=3^2 = 9$ and $(y_2 - y_1)^2=5^2 = 25$. Then $(x_2 - x_1)^2+(y_2 - y_1)^2=9 + 25=34$.

Step4: Take the square - root

$d=\sqrt{34}\approx5.8$ (rounded to the nearest tenth).

Answer:

$5.8$