Question

select the correct answer from each drop - down menu. valeries work deriving the distance formula for length d is shown. evaluate her work and explain any errors. she chose a point that a right angle. she wrote the length of each of the legs. she in the equation.

Explanation:

Step1: Analyze the right - angle condition

To form a right - triangle for the distance formula derivation, the point chosen should form a right - angle. If the vertical and horizontal segments are perpendicular, the point should be such that one segment is parallel to the x - axis and the other to the y - axis.

Step2: Check the leg lengths

The length of the horizontal leg should be \(|x_2 - x_1|\) (a non - negative quantity representing the horizontal distance between two points \((x_1,y_1)\) and \((x_2,y_2)\)) and the vertical leg should be \(|y_2 - y_1|\) (a non - negative quantity representing the vertical distance between two points).

Step3: Apply the Pythagorean theorem

By the Pythagorean theorem \(d^{2}=(x_2 - x_1)^{2}+(y_2 - y_1)^{2}\), so \(d=\sqrt{(x_2 - x_1)^{2}+(y_2 - y_1)^{2}}\). Valeria missed the square root in her formula.

Answer:

She chose a point that does not form a right - angle. She incorrectly wrote the length of each of the legs (should be absolute values). She forgot the square root in the equation.