Question

find the distance between the pair of points. give an exact answer, and where appropriate, an approximation to three decimal places. (-3,10) and (-4,13)

a. $sqrt{8}$, 2.828
b. $sqrt{10}$, 3.162
c. $sqrt{4}$, 2.000
d. $sqrt{20}$, 4.472

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 the given points

Let $(x_1,y_1)=(-3,10)$ and $(x_2,y_2)=(-4,13)$. Then $x_2 - x_1=-4-(-3)=-1$ and $y_2 - y_1=13 - 10 = 3$.

Step3: Calculate the distance

$d=\sqrt{(-1)^2+3^2}=\sqrt{1 + 9}=\sqrt{10}$.

Step4: Find the approximation

$\sqrt{10}\approx3.162$ (rounded to three decimal places).

Answer:

B. $\sqrt{10},3.162$