Line EF passes through the points (0,1) and (3,3). Line JK passes through the points (8,2) and (6,5) these lines are ?

Question

Is it a skew 

parallel

 

cocurrent 

or perpendicular.

Answer 1

Hi Kenzie, start by finding the slope of the two lines. The slope of line EF is:

 

Slope = (3 - 1) / (3 - 0) = 2 / 3

 

The slope of line JK is:

 

Slope = (5 - 2) / (6 - 8) = 3 / -2

 

If the lines are parallel, the slopes will be the same. The slope of line EF and line JK are not the same, therefore they are not parallel.

 

If the lines are perpendicular, the slopes will be the negative reciprocal of each other. Line EF is the negative reciprocal of line JK, therefore the lines are perpendicular to one another.

 

Another way to look at whether the lines are perpendicular is the slope of line EF times the slope of line JK will equal -1.

 

(2 / 3) * (3 / -2) = -1, since the 2 in the first term will cancel with the 2 in the second term, and the 3 in the first term will cancel with the 3 in the second term, leaving -1.

 

Questions?