Question

calculate the distance between the points q=(1, -9) and h=(9, -3) in the coordinate plane. give an exact answer (not a decimal approximation).

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 $(x_1,y_1)=(1,-9)$ and $(x_2,y_2)=(9,-3)$. Then $x_2 - x_1=9 - 1 = 8$ and $y_2 - y_1=-3-(-9)=-3 + 9 = 6$.

Step3: Calculate distance

$d=\sqrt{8^2+6^2}=\sqrt{64 + 36}=\sqrt{100}=10$.

Answer:

$10$