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

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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 | College Teacher | (Level 3) Valedictorian

Posted on

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.