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?
( d = sqrt{(x_2 - (-3))^2 + (y_1 - 0)^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: Identify given coordinates

From the graph, $(x_1,y_1)$ has $y_1=-4$, $(x_2,y_2)$ has $x_2=4, y_2=-3$. The reference point has $x=-2,y=0$.

Step3: Analyze Brian's error

Brian used $y_1-(0)$ instead of $y_2-y_1$, and $x_1-(-3)$ instead of $x_2-x_1$. He subtracted from the reference point coordinates instead of subtracting the two endpoints' coordinates directly, which is equivalent to misapplying the subtraction of coordinates (using a third point instead of the two segment endpoints).

Step4: Match to options

Option A states he subtracted coordinates incorrectly, which aligns with this error.

Answer:

A. He subtracted the coordinates instead of adding them to get the distance terms.