Answer:
31. Omission of the square root sign in step 1.
32. Subtracting the y-value from the x-value in each parentheses in step 1.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
Given points:
Question 31
The error was the omission of the square root sign in the first step of the calculation:
[tex]\textsf{Error}: \quad AB=(6-2)^2+(1-(-4))^2[/tex]
[tex]\textsf{Correction}: \quad AB=\sqrt{(6-2)^2+(1-(-4))^2}[/tex]
Correct calculation:
[tex]\begin{aligned}AB&=\sqrt{(6-1)^2+(2-(-4))^2}\\&=\sqrt{5^2+6^2}\\&=\sqrt{25+36}\\&=\sqrt{61}\\& \approx 7.8\end{aligned}[/tex]
Question 32
The error was subtracting the y-value from the x-value in each parentheses in the first step of the calculation, rather than subtracting the x-values and the y-values separately:
[tex]\begin{aligned}\textsf{Error}: \quad AB&=\sqrt{(x_A-y_A)^2+(x_B-y_B)^2}\\ &=\sqrt{(6-2)^2+(1-(-4))^2}\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Correction}: \quad AB&=\sqrt{(x_A-x_B)^2+(y_A-y_B)^2}\\&=\sqrt{(6-1)^2+(2-(-4))^2\end{aligned}[/tex]
Correct calculation:
[tex]\begin{aligned}AB&=\sqrt{(6-1)^2+(2-(-4))^2}\\&=\sqrt{5^2+6^2}\\&=\sqrt{25+36}\\&=\sqrt{61}\\& \approx 7.8\end{aligned}[/tex]
