Question

question 1 (1 point) find the distance between the points: (-4, 6) and (3, -7). please round your answer to 2 decimal places. distance = ______

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, $x_1=-4,y_1 = 6,x_2=3,y_2=-7$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=3-(-4)=7$, $y_2 - y_1=-7 - 6=-13$.

Step3: Square the differences

$(x_2 - x_1)^2=7^2 = 49$, $(y_2 - y_1)^2=(-13)^2=169$.

Step4: Sum the squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=49 + 169=218$.

Step5: Calculate the square - root

$d=\sqrt{218}\approx14.76$.

Answer:

$14.76$