Question

question
find the distance between the two points rounding to the nearest (if necessary).
(1, 2) and (-1, -7)

Explanation:

Step1: Identify distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Substitute values

Let $(x_1,y_1)=(1,2)$ and $(x_2,y_2)=(-1,-7)$. Then $x_2 - x_1=-1 - 1=-2$ and $y_2 - y_1=-7 - 2=-9$.

Step3: Calculate squared - terms

$(x_2 - x_1)^2=(-2)^2 = 4$ and $(y_2 - y_1)^2=(-9)^2 = 81$.

Step4: Sum squared - terms

$(x_2 - x_1)^2+(y_2 - y_1)^2=4 + 81=85$.

Step5: Find square - root

$d=\sqrt{85}\approx9.2$.

Answer:

$9.2$