Question

select the correct answer. fernando is using the distance formula to find the length, d, of the line segment. his work is shown on the graph. ( d = sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} ) what mistake did he make?

• he subtracted the wrong coordinates to find the distance of the horizontal leg.
• he squared the distance terms.
• he used a radical to find d.
• he subtracted the wrong coordinates to find the distance of the vertical leg.

Explanation:

To determine Fernando's mistake, we analyze the distance formula and his application. The distance formula for the vertical leg (change in \( y \)-coordinates) should use \( y_2 - y_1 \), but Fernando subtracted the wrong coordinates (e.g., used \( 4 - (-1) \) or similar incorrect subtraction for the vertical component instead of the correct \( y \)-coordinate difference). The option "He subtracted the wrong coordinates to find the distance of the vertical leg" matches this error, as the vertical leg's length depends on correct \( y \)-coordinate subtraction, and he messed up that subtraction. Other options: "subtracted wrong for horizontal" is incorrect (horizontal subtraction in the graph seems \( 3 - (-1) \) which is correct), "squared the distance terms" is not shown, "used a radical to find \( d \)" is part of the distance formula, so not a mistake.

Answer:

He subtracted the wrong coordinates to find the distance of the vertical leg.