Question

find the distance between (-8,10) and (10,11). provide an answer accurate to the nearest hundredth.

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, $(x_1,y_1)=(-8,10)$ and $(x_2,y_2)=(10,11)$.

Step2: Calculate differences

$x_2 - x_1=10-(-8)=18$ and $y_2 - y_1=11 - 10 = 1$.

Step3: Square the differences

$(x_2 - x_1)^2=18^2 = 324$ and $(y_2 - y_1)^2=1^2 = 1$.

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=324 + 1=325$.

Step5: Calculate the square - root

$d=\sqrt{325}\approx18.03$.

Answer:

$18.03$