Question

a horizontal line segment has a length of 6 units. one endpoint is on (-4,5). which could be the other endpoint? (-4, 11) the victim was not electrocuted. (2, 1) mr. epsilon was shadow boxing in the gym. (2, 5) chemical poisoning was not the cause of death. (10, 13) coach omega was replacing a broken window in the atrium.

Explanation:

Step1: Recall horizontal line property

A horizontal line segment has the same \( y \)-coordinate for both endpoints. The given endpoint is \((-4, 5)\), so the other endpoint must have \( y = 5 \).

Step2: Check distance formula

The distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \). For horizontal line, \( y_2 = y_1 \), so \( d = |x_2 - x_1| \). We need \( |x_2 - (-4)|=6 \), i.e., \( |x_2 + 4| = 6 \).

Step3: Solve for \( x_2 \)

Case 1: \( x_2 + 4 = 6 \Rightarrow x_2 = 2 \). Case 2: \( x_2 + 4=-6 \Rightarrow x_2=-10 \). So possible \( x \)-coordinate is \( 2 \) (since \(-10\) isn't an option here), and \( y = 5 \). So the point is \((2, 5)\).

Answer:

\((2, 5)\)