Question

describe the error in finding the distance between a(6, 2) and b(1, -4). ab=(6 - 1)^2+2-(-4)^2 = 5^2+6^2 = 25 + 36 = 61. 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 $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_1 - x_2)^2+(y_1 - y_2)^2}$. For points $A(6,2)$ and $B(1, - 4)$, the correct formula application gives $(6 - 1)^2+(2-(-4))^2$ as part of the calculation inside the square - root. But the given work stopped after calculating $(6 - 1)^2+(2-(-4))^2$ and did not take the square root.

Step2: Calculate correct distance

First, calculate $(6 - 1)^2+(2-(-4))^2=5^2 + 6^2=25 + 36=61$. Then, $AB=\sqrt{61}\approx 7.8$ (rounded to the nearest tenth).

Answer:

The error is: Did not take the square root.
The actual length, $AB$, rounded to the nearest tenth is $7.8$ units.