Question

find the distance between the pair of points.
(3, 4) and (0, 8)
a) 6
b) 25
c) 10
d) 5

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 $(x_1,y_1)=(3,4)$ and $(x_2,y_2)=(0,8)$. Then $x_2 - x_1=0 - 3=- 3$ and $y_2 - y_1=8 - 4 = 4$.

Step3: Calculate the squares

$(x_2 - x_1)^2=(-3)^2 = 9$ and $(y_2 - y_1)^2=4^2 = 16$.

Step4: Sum the squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=9 + 16=25$.

Step5: Take the square - root

$d=\sqrt{25}=5$.

Answer:

D. 5