Question

brian sets up the distance formula to find the length, d, of the line segment. his work is shown. what error, if any, did brian make?
image of a coordinate plane with two points and a distance formula setup
$d = \sqrt{(x_2 - (-3_1))^2 + (y_1 - (0_1))^2}$
a. he subtracted the coordinates instead of adding them to get the distance terms.
b. the point he chose to draw the legs of the triangle does not form a right angle.
c. he incorrectly found d, instead of $d^2$.
d. he incorrectly squared each distance term.

Explanation:

Step1: Recall Distance Formula

The distance formula 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: Analyze Brian's Work

Brian used \((x_2-(-3))\) (implying \(x_1=-3\)) and \((y_1 - 0)\) (implying \(y_2 = 0\)), but in the distance formula, it should be \((x_2 - x_1)\) and \((y_2 - y_1)\). The point he chose to form the right triangle (the dashed lines) does not form a right angle with the two given points, because the vertical and horizontal legs should be parallel to the axes and connect the two points, but his chosen point does not satisfy that.

Check other options:

• Option A: The distance formula uses subtraction, so this is wrong.
• Option C: He used the square - root (for \(d\)), which is correct for distance, so this is wrong.
• Option D: Squaring the distance terms is part of the distance formula, so this is wrong.

Answer:

B. The point he chose to draw the legs of the triangle does not form a right angle.