Question

error analysis describe the error in finding the distance between a(6, 2) and b(1, - 4). did not use a ruler. did not find the midpoint. did not take the square root. did not make all the signs positive. the actual length, ab, rounded to the nearest tenth is units.

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Given $A(6,2)$ and $B(1,-4)$, we have $x_1 = 6,y_1=2,x_2 = 1,y_2=-4$. The correct calculation should be $AB=\sqrt{(6 - 1)^2+(2-(-4))^2}=\sqrt{5^2 + 6^2}=\sqrt{25 + 36}=\sqrt{61}$. The given work only calculated $(6 - 1)^2+(2-(-4))^2=61$ without taking the square - root.

Answer:

Did not take the square root.
The actual length, $AB$, rounded to the nearest tenth is $\sqrt{61}\approx 7.8$ units.