Question

find the distance between points. 1) a ( 3,4 ) and b ( 7,1 )

Explanation:

Step1: Recall distance formula

The distance \( d \) 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 \( A(3,4) \) and \( B(7,1) \), \( x_1 = 3,y_1 = 4,x_2 = 7,y_2 = 1 \).

Step3: Substitute into formula

\( d=\sqrt{(7 - 3)^2+(1 - 4)^2}=\sqrt{4^2+(- 3)^2}=\sqrt{16 + 9}=\sqrt{25} \).

Step4: Simplify

\( \sqrt{25}=5 \).

Answer:

5