Question

question 13
score: 0 of 1 point
find the distance between (-18, 3) and (5, 19). make sure you fully simplify your radical answer.
distance = enter your answer √
submit answer
show answers
find this question difficult? do you know you can practice another version of this question?

Explanation:

Step1: Identify the 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, \(x_1=-18,y_1 = 3,x_2=5,y_2=19\).

Step2: Substitute the values into the formula

Substitute the values: \((x_2 - x_1)=5-(-18)=5 + 18=23\) and \((y_2 - y_1)=19 - 3=16\). Then \(d=\sqrt{23^2+16^2}\).

Step3: Calculate the squares

\(23^2 = 529\) and \(16^2=256\). So \(d=\sqrt{529 + 256}\).

Step4: Add the values inside the square - root

\(529+256 = 785\). Now, factorize \(785\): \(785=5\times157\) (since \(157\) is a prime number).

Answer:

\(\sqrt{785}\)