Question

question 6 (1 point)
what is the distance between (7, -1) and (-5, -6)?
$d = 14$ units
$d = 13$ units
$d = 12$ units
$d = 11$ units

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: Assign values

Let $(x_1,y_1)=(7,-1)$ and $(x_2,y_2)=(-5,-6)$. Then $x_2 - x_1=-5 - 7=-12$ and $y_2 - y_1=-6-(-1)=-5$.

Step3: Calculate squares and sum

$(x_2 - x_1)^2=(-12)^2 = 144$ and $(y_2 - y_1)^2=(-5)^2 = 25$. The sum is $144 + 25=169$.

Step4: Calculate square - root

$d=\sqrt{169}=13$.

Answer:

B. $d = 13$ units