A, B, C, and D have the coordinates (-8, 1), (-2,4),(-3,-1) and (-6,5), respectively. Which sentence about the points is true?A. A, B, C, and D lie on the same lineB. AB and CD are perpendicular lines.c. Ag and are parallel lines.D. AB and CD are intersecting lines but are not perpendicular.E. AC and B are parallel lines.

Accepted Solution

Answer:B. [tex]^\leftrightarrow_{AB}[/tex] and [tex]^\leftrightarrow_{CD}[/tex]  are perpendicular lines.Step-by-step explanation:We can quickly plot the points in the cartesian plane as shown in the attachment.A visual representation will help us see that A,B,C, and D do not lie on the same line.The slope of AB  is [tex]\frac{4-1}{-2--8} =\frac{3}{6}=\frac{1}{2}[/tex]The slope of CD is [tex]\frac{5--1}{-6--3} =\frac{6}{-3}=-2[/tex]The two slopes are negative reciprocals of each other.It is true that line AB and line CD are perpendicular.These two lines cannot be perpendicular and parallel at the same time.It is also not possible that, the two lines are perpendicular but will not intersectTherefore the correct choice is B