Question

what is the distance between $(8, -3)$ and $(4, -7)$?
choose 1 answer:
a 6
b 9
c $\sqrt{32}$
d $\sqrt{42}$

Explanation:

Step1: Recall the 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, \(x_1 = 8,y_1=-3,x_2 = 4,y_2=-7\).

Step2: Substitute the values into the formula

\(d=\sqrt{(4 - 8)^2+(-7+3)^2}=\sqrt{(-4)^2+(-4)^2}\).

Step3: Simplify the expression

\(d=\sqrt{16 + 16}=\sqrt{32}\).

Answer:

C. \(\sqrt{32}\)