Perpendicular Lines in the Co ordinate Plane:
What is a Co-ordinate plane?
A coordinate plane is a fundamental concept of coordinate geometry, which describes a two-dimensional plane in terms of two perpendicular axes x and y along the horizontal and vertical direction of the plane.
What is a Slope?
The slant of a line on the coordinate plane is referred to as the slope. It is ratio of the change in the y-value to the change in the x-value, i.e.,
Slope = Change in y-value/Change in x-value
What is a Y-intercept?
The point where the line meets the y-axis is referred to as the Y-intercept.
What is the equation of a line?
The equation of a line, in co-ordinate geometry, can be written as:
Y = mx + c
Where m = slope and c = y-intercept
What is a negative slope?
If the slope m has a negative value, then it is referred to as negative slope.
When are two lines said to be perpendicular?
Two vertical lines are said to be perpendicular if and only if the product of their slopes is -1. This means, if the slope of one of the lines is the negative reciprocal of the other, then the two lines are said to be perpendicular.
That is, if the slope of one line is m, then the slope of the other is -1/m. When two lines are perpendicular to each other, their slopes share a particular relationship with each other. Conversely, if the slopes of 2 lines are negative reciprocals of each other, then the lines are said to be perpendicular.
Another point to keep in mind is that lines do not have to intersect to be perpendicular ie the slope relationship still holds well.
Both vertical and horizontal lines are perpendicular to each other.
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