Question

Exercise#1: Line segment AB has endpoints (-2,-1) and (1,8). What is the equation for the perpendicular line of line AB. A. Y=1/3X +3 B. 2y= -x + 4.7 C. y= 1/2 x +3 D. 2x= -6y +3 Students choose an option

Answer 1

Given a line made by two points (x1, y1) and (x2, y2), its slope (m) is computed as:

`m\text{ = }(y_2-y_1)/(x_2-x_1)`

In this case, the points are (-2, -1) and (1, 8). The slope is:

`m_1\text{ = }\frac{8\text{ - (-1)}}{1\text{ - (-2)}}=(9)/(3)=3`

Two lines are perpendicular if the multiplication of their slopes is equal to -1. Then:

`\begin{gathered} m_1\cdot m_2=-1 \\ m_2\text{ = }(-1)/(m_1) \\ m_2\text{ = }(-1)/(3) \end{gathered}`

Isolating y in option D:

2x = -6y +3

2x - 3 = -6y

2/(-6)x - 3/(-6) = y

-1/3x + 1/2 = y

where -1/3 is its slope. Then, this line is perpendicular to line segment AB