Question

1. given points a(1, 3) and b(4, 7), what is the distance between them? 5 units 6 units 3 units 4 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 the values

Here $x_1 = 1,y_1 = 3,x_2 = 4,y_2 = 7$. So $d=\sqrt{(4 - 1)^2+(7 - 3)^2}=\sqrt{3^2+4^2}$.

Step3: Calculate the squares and sum

$3^2=9$, $4^2 = 16$, and $9 + 16=25$. So $d=\sqrt{25}$.

Step4: Find the square - root

$\sqrt{25}=5$.

Answer:

A. 5 units