In order for two lines to be perpendicular, they must intersect at a 90-degree angle. This means that the slope of one line must be the negative reciprocal of the slope of the other line. In other words, if one line has a slope of m, the other line must have a slope of -1/m.
No, two lines cannot be perpendicular if they have the same slope. As mentioned before, for two lines to be perpendicular, their slopes must be the negative reciprocal of each other. If two lines have the same slope, they are parallel and do not intersect at a 90-degree angle.
To verify that two lines are perpendicular algebraically, you can use the formula for finding the slope of a line: m = (y2 - y1) / (x2 - x1). Plug in the coordinates of two points on each line and calculate the slopes. If the slopes are negative reciprocals of each other, the lines are perpendicular.
Graphically, perpendicular lines will intersect at a 90-degree angle and form a cross or "T" shape. The slopes of the lines will also be negative reciprocals of each other. Additionally, if you were to extend the lines infinitely, they would never intersect.
Yes, two lines can be perpendicular if one is horizontal and the other is vertical. In this case, the horizontal line would have a slope of 0 and the vertical line would have an undefined slope. Their slopes would be negative reciprocals of each other (-1/0 and 0/-1, respectively).