relative positionDetermine if the line through (1,1) and (3,2) is perpendicular to the line through (-2,4) and (-2,5)?

Expert Answers
justaguide eNotes educator| Certified Educator

The slope of a line through the points (x1, y1) and (x2, y2) is given by m = (y2 - y1)/(x2 - x1). Two lines are perpendicular if the product of the slope is -1.

Here the slope of the line through (1,1) and (3,2) is: (2-1)/(3-1) = 1/2

That of the line through (-2,4) and (-2,5) is : (5-4)/0 = inf.

If the slope is perpendicular the line is vertical, but the other line is not horizontal. Therefore they are not perpendicular.

giorgiana1976 | Student

We'll have to calculate the slopes of the given lines, to decide if they are perpendicular.

Slope of line through the points  (1,1) and (3,2) is:

m1= (y2-y1)/(x2-x1)

x1=1,y1=1,x2=3,y2=2

m1 = (2-1)/(3-1)

m1 = 1/2

Now, we'll consider the next two points (-2,4) and (-2,5).

m2 = (5-4)/(-2+2)

m2 =1/0 undefined (the line is parallel to y axis)

This line is perpendicular to x axis and not to the line whose slope is 1/2.