Question

error analysis describe the error in finding the distance between a(6, 2) and b(1, - 4). did not average x - coordinates and y - coordinates to find the midpoint. did not find differences of the x - values and of the y - values. did not make all signs positive before subtraction. did not take the absolute value of the differences. the actual length, ab, 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 $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $A(6,2)$ and $B(1,- 4)$, we need to find differences of $x -$values and $y -$values. The error in the given work is that it did not find differences of the $x -$values and of the $y -$values correctly.

Step2: Calculate differences

$x_1 = 6,y_1 = 2,x_2 = 1,y_2=-4$. The difference in $x -$values is $x_2 - x_1=1 - 6=-5$ and the difference in $y -$values is $y_2 - y_1=-4 - 2=-6$.

Step3: Apply distance formula

$d=\sqrt{(1 - 6)^2+(-4 - 2)^2}=\sqrt{(-5)^2+(-6)^2}=\sqrt{25 + 36}=\sqrt{61}\approx 7.8$

Answer:

The correct option for the error is: Did not find differences of the $x -$values and of the $y -$values. The actual length $AB$ to the nearest tenth is $7.8$ units.