Question

find the distance between the points (-20, 15) and (-10, 5). round decimals to the nearest tenth.

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, $(x_1,y_1)=(-20,15)$ and $(x_2,y_2)=(-10,5)$.

Step2: Calculate differences

$x_2 - x_1=-10-(-20)=-10 + 20=10$ and $y_2 - y_1=5 - 15=-10$.

Step3: Square the differences

$(x_2 - x_1)^2=10^2 = 100$ and $(y_2 - y_1)^2=(-10)^2=100$.

Step4: Sum squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=100 + 100=200$.

Step5: Calculate square - root

$d=\sqrt{200}\approx14.142$.

Step6: Round to nearest tenth

Rounding $14.142$ to the nearest tenth gives $14.1$.

Answer:

$14.1$