Item 4 Question 1 Determine of which lines, if any, are parallel or perpendicular. Explain. Line a passes through (−2, 1) and (0, 3) . Line b passes through (4, 1) and (6, 4) . Line c passes through (1, 3) and (4, 1) .

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:

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)

Let m2 be the slope of line b which passes through (4, 1) and (6, 4)

Let m3 be the slope of line c which passes through (1, 3) and (4, 1)

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

Hence,

Line b and line c are perpendicular.