Question

george calculated the distance between (2,4) and (6,3) using the distance formula.

georges work

1. ( d=sqrt{(6 - 2)^2+(3 - 4)^2} )
2. ( d=sqrt{(4)^2+( - 1)^2} )
3. ( d=sqrt{16 + 1} )
4. ( d=sqrt{17} )

analyze georges work. is he correct? if not, what was his mistake?

yes, he is correct.

no, he substituted values in the wrong places.

no, he didnt use the proper order of operations.

no, he evaluated the powers incorrectly.

Explanation:

Step1: Recall 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, \((x_1,y_1)=(2,4)\) and \((x_2,y_2)=(6,3)\). Substituting into the formula gives \(d=\sqrt{(6 - 2)^2+(3 - 4)^2}\), which is George's step 1.

Step2: Simplify the expressions inside the square - root

\(6−2 = 4\) and \(3−4=-1\), so \(d=\sqrt{4^2+(-1)^2}\), which is George's step 2.

Step3: Evaluate the squares

\(4^2 = 16\) and \((-1)^2 = 1\), then \(d=\sqrt{16 + 1}\), which is George's step 3.

Step4: Add the numbers inside the square - root

\(16+1=17\), so \(d = \sqrt{17}\), which is George's step 4.

Answer:

Yes, he is correct.