Question

brian found the distance between (2,-6) and (3,2) to be 9. his work is below, what did he do wrong?
\\( \sqrt { ( 3 - 2 ) ^ { 2 } + ( 2 - ( - 6 ) ) ^ { 2 } } = \sqrt { 1 ^ { 2 } + 8 ^ { 2 } } = 1 + 8 = 9 \\)
he didnt do anything wrong.
he should have added the xs and ys, but he subtracted.
he should have squared 1 and 8 before taking the square root.
he should have gotten 4 instead of 8 for the y differences.

Explanation:

Step1: Recall the distance formula

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

Step2: Analyze Brian's work

For the points \((2,-6)\) and \((3,2)\), \(x_2 - x_1=3 - 2 = 1\) and \(y_2 - y_1=2-(-6)=8\). Then, by the distance formula, \(d=\sqrt{1^2 + 8^2}=\sqrt{1 + 64}=\sqrt{65}\).

Step3: Identify the error

Brian made a mistake in the step \(\sqrt{1^2+8^2}=1 + 8\). He should have calculated \(1^2=1\), \(8^2 = 64\), then \(1+64 = 65\) and finally \(\sqrt{65}\), not \(1+8\). He skipped squaring \(1\) and \(8\) before adding and taking the square - root.

Answer:

C. He should have squared 1 and 8 before taking the square root.