Question

in exercises 21 - 28, find the distance between the two points. 21. a(13,2) and b(7,10) 22. c(-6,5) and d 23. e(3,7) and f(6,5) 24. g(-5,4) and h 25. j(-8,0) and k(1,4) 26. l(7,-1) and m

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 points for problem 23

For points $E(3,7)$ and $F(6,5)$, $x_1 = 3,y_1 = 7,x_2 = 6,y_2 = 5$.

Step3: Substitute values into formula

$d=\sqrt{(6 - 3)^2+(5 - 7)^2}=\sqrt{3^2+( - 2)^2}=\sqrt{9 + 4}=\sqrt{13}$.

Answer:

$\sqrt{13}$