By definition, A perpendicular line is a line that makes 90 degrees(right angle) with another line. It doesn't state whether it passes through or not. So, the answer to the question, is it depends. If there is a figure, follow it.
Chat with our AI personalities
Parallel lines run in the same direction. If they are intersected by one line and that line is perpendicular to both, then it proves that the lines run parallel to each other.
The slope (rise over run) of one line will be a number (n) or (-n) and the perpendicular line's slope will be the exact opposite. So, for instance, if one line has a slope of 2/3, then a perpendicular line's slope must be -2/3, and vice versa.
Oblique
The slope of a line perpendicular to the line through (0,5) and (-3,-4) will have a slope that is "opposite" that of the first line, which will be the negative inverse of the slope of the first line, which is -[1/slope] of the first line. So let's find the slope of that first line and then invert it and change its sign to find the slope of a line perpendicular to it. A line through the points (0,5) and (-3,-4) will have a slope that can be found by a simple formula. We take the change of y divided by the change of x and it's that simple. It's that "rise over run" thing that you may have heard of. Ready? Let's jump. The change of y is the "rise" and the change of x is the "run" in the expression. Using the points given, the rise is from 5 to -4, or -9. (To get from 5 to -4, you have to go 9 units in the - or negative direction.) The run is from 0 to -3 or -3. (To get from 0 to -3, you have to go 3 units in the - or negative direction.) The rise over the run is -9/-3 or 9/3 or 3/1 or 3. Piece of cake. Let's do it the other way around to be sure you've got it, okay? Switch the coordinates from (0,5) and (-3,-4) to (-3,-4) and (0,5) and work it. The rise or change of y is from -4 to 5, which is a rise of 9 in the + or positive direction, or +9. The run or change of x is from -3 to 0, which is a run of 3 in the + or positive direction, or +3. The rise over the run is +9/+3 = 9/3 = 3/1 = 3. The slopes match. And why wouldn't they? Onward. We need to take the negative inverse of that slope to find a line perpendicular to it. Let's do that and be done with our problem. A line perpendicular to another line with the slope 3 will have a slope of - (1/3) or - 1/3 or negative 1/3rd or a negative one third. The slope of a line perpendicular to a line through (0,5) and (-3,-4) is - 1/3 or negative one third.
Parallel lines are lines that run side by side and never meet. Perpendicular lines are lines that meet in one point, forming four right angles around the point.