what is the condition for parallel lines
Answers
Answer:
Two lines in a plane are said to be parallel if they do not intersect, when extended infinitely in both the direction. Also, the distance between the two lines is the same throughout. The symbol for denoting parallel lines is ∥.
Answer:
(i) Condition for the lines to be parallel in terms of their slopes.
Let m1 and m2 be the slopes of two lines.
If the two lines are parallel, then their slopes will be equal.
That is,
m1 = m2
(ii) Condition for the lines to be parallel in terms of their general form of equations.
Let us consider the general form of equation of a straight line.
ax + by + c = 0
If the two lines are parallel, then their general forms of equations will differ only in the constant term and they will have the same coefficients of x and y.
That is,
ax + by + c1 = 0
ax + by + c2 = 0
(iii) Condition for the lines to be parallel in terms of their slope-intercept form of equations.
Let us consider the slope intercept form of equation of a straight line.
y = mx + b
If the two lines are parallel, then their slope-intercept form equations will will differ only in the "y"- intercept.
That is,
y = mx + b1
y = mx + b2
(iv) Condition for the lines to be parallel in terms of angle of inclination.
Let l1 and l2 be two lines.
If the two lines are parallel, the angle between them and the positive side of x-axis will be equal.
(v) Condition for the lines to be parallel in terms of the perpendicular distance between them.
If the two lines are parallel, the perpendicular distance between them will be same at everywhere.
(vi)Condition for the lines to be parallel when they are cut by a transversal.
Step-by-step explanation:
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