Question

coordinates (x1, y1) of point q: (-9, 4)
coordinates (x2, y2) of point r: (3, -7)
d = \sqrt{(x2 - x1)^2+(y2 - y1)^2}
d = \sqrt{(-12)^2+(11)^2}
d =
the length of segment qr is yards

Explanation:

Step1: Calculate differences

$x_2 - x_1=3-(-9)=12$, $y_2 - y_1=-7 - 4=-11$. But in the given work, they are likely considering the order as $x_1 - x_2=-9 - 3=-12$ and $y_1 - y_2=4-(-7)=11$.

Step2: Calculate the square - sum

$d=\sqrt{(-12)^2+(11)^2}=\sqrt{144 + 121}=\sqrt{265}$

Answer:

$\sqrt{265}$