Question

calculate the distance between the points q=(-8, 9) and e=(-1, 1) in the coordinate plane. round your answer to the nearest hundredth.

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, $(x_1,y_1)=(-8,9)$ and $(x_2,y_2)=(-1,1)$.

Step2: Calculate differences

$x_2 - x_1=-1-(-8)=7$ and $y_2 - y_1=1 - 9=-8$.

Step3: Square differences

$(x_2 - x_1)^2=7^2 = 49$ and $(y_2 - y_1)^2=(-8)^2 = 64$.

Step4: Sum squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=49 + 64=113$.

Step5: Calculate square - root

$d=\sqrt{113}\approx10.63$.

Answer:

$10.63$