Question

1. -/1 points find the distance between the two points. simplify your answer, and write the exact answer in simplest radical form for irrational answers. (x, y) = (-4, 5) and (x, y) = (1, -8) resources ebook example video

Explanation:

Step1: Identify the 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, $(x_1,y_1)=(-4,5)$ and $(x_2,y_2)=(1, - 8)$.

Step2: Calculate the differences

First, find $x_2 - x_1$ and $y_2 - y_1$.
$x_2 - x_1=1-(-4)=1 + 4=5$.
$y_2 - y_1=-8 - 5=-13$.

Step3: Square the differences and sum them

$(x_2 - x_1)^2=5^2 = 25$ and $(y_2 - y_1)^2=(-13)^2 = 169$.
The sum is $(x_2 - x_1)^2+(y_2 - y_1)^2=25 + 169=194$.

Step4: Find the distance

$d=\sqrt{194}$.

Answer:

$\sqrt{194}$