Answer:
Line b and line c are perpendicular.
Step-by-step explanation:
In order to find if the lines are parallel, perpendicular or neither, their slopes have to be found.
Slope is denoted by m and is calculated as:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Here (x1,y1) and (x2,y2) are the coordinates of the point through which the line passes.
Let m1 be the slope of line a
and line a passes through (−2, 1) and (0, 3)
[tex]m_1 = \frac{3-1}{0+2} = \frac{2}{2} = 1[/tex]
Let m2 be the slope of line b which passes through (4, 1) and (6, 4)
[tex]m_2 = \frac{4-1}{6-4} = \frac{3}{2}[/tex]
Let m3 be the slope of line c which passes through (1, 3) and (4, 1)
[tex]m_3 = \frac{1-3}{4-1} = \frac{-2}{3}[/tex]
When two lines are parallel, their slopes are equal.
When two lines are parallel, the product of their slope is -1
None of the slopes are equal to each other so none of the lines are parallel
And
[tex]m2.m3\\= \frac{3}{2} * -\frac{2}{3}\\= -1[/tex]
Hence,
Line b and line c are perpendicular.
