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(-3,1) 23. e(3,7) and f(6,5) 24. g(-5,4) and h(2,6) 25. j(-8,0) and k(1,4) 26. l(7,-1) and m(-2,4) 27. r(0,1) and s(6,3.5) 28. t(13,1.6) and v(5.4,3.7)

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: For point $E(3,7)$ and $F(6,5)$

Let $(x_1,y_1)=(3,7)$ and $(x_2,y_2)=(6,5)$. Then $x_2 - x_1=6 - 3 = 3$ and $y_2 - y_1=5 - 7=- 2$.

Step3: Calculate the squares

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

Step4: Sum the squares and take square - root

$d=\sqrt{9 + 4}=\sqrt{13}$.

Answer:

$\sqrt{13}$