Question

select the correct answer.
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 a line segment, a dashed triangle, and the distance formula setup
a. he incorrectly squared each distance term.
b. he subtracted the coordinates instead of adding them to get the distance terms.
c. the point he chose to draw the legs of the triangle does not form a right angle.
d. he incorrectly found d, instead of ( d^2 ).

Explanation:

Step1: Recall the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). In this formula, we subtract the \(x\) - coordinates and \(y\) - coordinates of the two points.

Step2: Analyze the right - triangle formation

To use the distance formula (which is based on the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse of a right - triangle and \(a\) and \(b\) are the legs), the legs of the right - triangle must be perpendicular (form a right - angle). The horizontal and vertical lines (used to form the legs of the right - triangle for the distance formula) should be perpendicular. In Brian's work, the point \(Q\) does not form a right - angle with the line segment \(d\). The horizontal and vertical displacements should be such that one is parallel to the \(x\) - axis and the other is parallel to the \(y\) - axis.

Answer:

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