Help your students prepare for their Maths GCSE with this free parallel and perpendicular lines worksheet of 30+ questions and answers
Parallel lines are lines that are the same distance apart and never meet. If we are thinking about straight lines on a graph, we know that the gradient of the line determines how steep the line is and what direction it is going in. For this reason, the equations of parallel lines have equal gradients. To identify parallel lines, we look at the gradients of the pair of lines, the gradients are the same then the lines are parallel.
Perpendicular lines are lines which meet at a right angle, i.e. the angle between the lines is 90o. The gradients of perpendicular lines are negative reciprocals of each other which means that if we multiply the two gradients, their product will be -1.
If we are given the equation of a line, we can work out the equation of lines which are parallel and perpendicular to it. First we must ensure the equation of the line is in the form y=mx+c.
The equation of a line parallel to y=3x+4, for example, would also have a gradient of 3. Therefore any line with equation y=3x+c would be parallel to the given line. The gradient of a perpendicular line would be the negative reciprocal of 3 which is -1/3., so any line with equation y=(-1/3)x + c would be perpendicular to the line y=3x+4.
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