Question

find the distance d(a,b) between points a and b. a(13,8); b(-2,28) d(a,b)= (simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Identify distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 13,y_1=8,x_2=-2,y_2 = 28$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=-2 - 13=-15$ and $y_2 - y_1=28 - 8 = 20$.

Step3: Square the differences

$(x_2 - x_1)^2=(-15)^2 = 225$ and $(y_2 - y_1)^2=20^2=400$.

Step4: Sum the squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=225 + 400=625$.

Step5: Take the square - root

$d(A,B)=\sqrt{625}=25$.

Answer:

$25$