Question

what is the distance between (-2, -1) and (1, 4)? provide an answer accurate to the nearest tenth.

Explanation:

Step1: Recall 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, $x_1=-2,y_1 = - 1,x_2=1,y_2 = 4$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=1-(-2)=3$ and $y_2 - y_1=4 - (-1)=5$.

Step3: Square the differences

Square the results from step 2. $(x_2 - x_1)^2=3^2 = 9$ and $(y_2 - y_1)^2=5^2 = 25$.

Step4: Sum the squares

Add the squared - values: $(x_2 - x_1)^2+(y_2 - y_1)^2=9 + 25=34$.

Step5: Calculate the square - root

$d=\sqrt{34}\approx5.83$.

Step6: Round to nearest tenth

Rounding $5.83$ to the nearest tenth gives $5.8$.

Answer:

$5.8$