Question

your friend calculates the distance between points q(1,5) and r(3,8), as shown below. what is his error? d = √((1 - 8)²+(5 - 3)²) = √((-7)²+(2)²) = √(49 + 4) = √53 ≈ 7.3 choose the correct answer below. a. in the first row, he wrote out the distance formula incorrectly. this row should be √((1 + 8)²-(5 + 3)²). b. in the first row, he substituted the coordinates of q and r into the formula incorrectly. this row should instead be √((1 - 3)²+(5 - 8)²). c. in the second row, he combined terms inside the parentheses incorrectly. this row should instead be √((9)²+(2)²). d. none of the above. his reasoning is correct.

Explanation:

Step1: Recall distance formula

The distance formula 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 $Q(1,5)$ and $R(3,8)$, we should have $d=\sqrt{(1 - 3)^2+(5 - 8)^2}$.

Step2: Analyze the error in first - row

The first - row error: He wrote $\sqrt{(1-8)^2+(5 - 3)^2}$, which is an incorrect substitution into the distance formula. He mixed up the $x$ and $y$ coordinates of the two points when substituting into the formula. It should be $\sqrt{(1 - 3)^2+(5 - 8)^2}$ instead.

Step3: Analyze the error in second - row

The second - row error: After the first - row error, in the second row when simplifying $(1 - 8)^2+(5 - 3)^2$, he combined terms inside the parentheses incorrectly. But the root of the problem is the wrong substitution in the first row.

Answer:

A. In the first row, he wrote out the distance formula incorrectly. This row should instead be $\sqrt{(1 - 3)^2+(5 - 8)^2}$