Question

calculate the distance between the points p = (-1, -4) and c = (3, -9) in the coordinate plane. give an exact answer (not a decimal approximation).

Explanation:

Step1: Recall distance formula

For points $(x_1,y_1)$ and $(x_2,y_2)$, distance $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step2: Assign coordinates

Let $(x_1,y_1)=(-1,-4)$, $(x_2,y_2)=(3,-9)$

Step3: Compute $x$-difference and square

$x_2-x_1=3-(-1)=4$, $(4)^2=16$

Step4: Compute $y$-difference and square

$y_2-y_1=-9-(-4)=-5$, $(-5)^2=25$

Step5: Sum squares and take root

$d=\sqrt{16+25}=\sqrt{41}$

Answer:

$\sqrt{41}$