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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

Sagot :

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

[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]

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

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

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

[tex]\begin{gathered} m_1\cdot m_2=-1 \\ m_2\text{ = }\frac{-1}{m_1} \\ m_2\text{ = }\frac{-1}{3} \end{gathered}[/tex]

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

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