Question

find the distance between c(5, -3) and d(4, -2).
a) $sqrt{4}$ or about 2 units
b) $sqrt{2}$ or about 1.4 units
c) $sqrt{3}$ or about 1.7 units
d) $sqrt{5}$ or about 2.2 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: Substitute coordinates

Here, $(x_1,y_1)=(5,-3)$ and $(x_2,y_2)=(4,-2)$. So $d=\sqrt{(4 - 5)^2+(-2-(-3))^2}$.

Step3: Simplify expression

First, calculate $(4 - 5)^2=(-1)^2 = 1$ and $(-2-(-3))^2=(-2 + 3)^2=1^2 = 1$. Then $d=\sqrt{1 + 1}=\sqrt{2}$.

Answer:

B. $\sqrt{2}$ or about 1.4 units