Question

trig/pre - calc test review: sections 1.1 - 1.5

1. find the distance between a and b. write answers in simplest form. a(5,2); b(3,8)
2. a(-2,-3); b(2,1)

Explanation:

Step1: Recall 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: Identify coordinates for problem 1

For points $A(5,2)$ and $B(3,8)$, $x_1 = 5,y_1 = 2,x_2 = 3,y_2 = 8$.

Step3: Substitute values into formula for problem 1

$d=\sqrt{(3 - 5)^2+(8 - 2)^2}=\sqrt{(- 2)^2+6^2}=\sqrt{4 + 36}=\sqrt{40}=2\sqrt{10}$.

Step4: Identify coordinates for problem 2

For points $A(-2,-3)$ and $B(2,1)$, $x_1=-2,y_1 = - 3,x_2 = 2,y_2 = 1$.

Step5: Substitute values into formula for problem 2

$d=\sqrt{(2-(-2))^2+(1 - (-3))^2}=\sqrt{(2 + 2)^2+(1 + 3)^2}=\sqrt{4^2+4^2}=\sqrt{16 + 16}=\sqrt{32}=4\sqrt{2}$.

Answer:

1. $2\sqrt{10}$
2. $4\sqrt{2}$