Question

find the distance between the points (-10, 2) and (-5, 7). round decimals to the nearest tenth. units

Explanation:

Step1: Identify 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, $x_1=-10,y_1 = 2,x_2=-5,y_2 = 7$.

Step2: Calculate differences

$x_2 - x_1=-5-(-10)=-5 + 10 = 5$ and $y_2 - y_1=7 - 2 = 5$.

Step3: Square the differences

$(x_2 - x_1)^2=5^2 = 25$ and $(y_2 - y_1)^2=5^2 = 25$.

Step4: Sum the squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=25 + 25=50$.

Step5: Calculate the square - root

$d=\sqrt{50}\approx7.1$ (rounded to the nearest tenth).

Answer:

$7.1$