Question

select the correct answer. heather’s work to find the distance between two points, ( r(-3,-4) ) and ( s(5,7) ), is shown: ( \begin{align} overline{rs} &= sqrt{((-4) - (-3))^2 + (7 - 5)^2} \\ &= sqrt{(-1)^2 + (2)^2} \\ &= sqrt{1 + 4} \\ &= sqrt{5} end{align} ) what error, if any, did heather make? a. she substituted incorrectly into the distance formula. b. she subtracted the coordinates instead of adding them. c. she made a sign error when simplifying inside the radical. d. she made no errors.

Explanation:

Step1: Recall distance formula

The distance 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: Substitute correct coordinates

For $R(-3,-4)$ and $S(5,7)$:
$$\sqrt{(5-(-3))^2+(7-(-4))^2}=\sqrt{(8)^2+(11)^2}$$

Step3: Identify Heather's error

Heather substituted $(-4)-(-3)$ for the $x$-coordinate difference instead of $5-(-3)$, and $7-5$ for the $y$-coordinate difference instead of $7-(-4)$. She mixed up $x$ and $y$ values in substitution.

Answer:

A. She substituted incorrectly into the distance formula.