Q. 565.0( 1 Vote )
State whether the statements are true or false.
Line joining the points (3, – 4) and (– 2, 6) is perpendicular to the line joining the points (–3, 6) and (9, –18).
Answer :
Given points are (3, -4), (-2, 6), (-3, 6) and (9, -18)
Now, we find the slope because if the lines are perpendicular then the product of the slopes is -1 i.e. m1m2 = -1
Slope of the line joining the points (3, -4) and (-2, 6)
Here, x1 = 3, x2 = -2, y1 = -4 and y2 = 6
⇒ m1 = -2
Now, slope of the line joining the points (-3, 6) and (9, -18)
Here, x1 = -3, x2 = 9, y1 = 6 and y2 = -18
⇒ m2 = -2
∵ m1 = m2 = -2
and m1m2 = -2 × (-2) = -4 ≠ -1
So, the lines are parallel and not perpendicular
Hence, the given statement is FALSE
Rate this question :
Various Forms of Equations of line45 mins
Parametric Equations of Straight line48 mins
Slope, inclination and angle between two lines48 mins
Interactive Quiz on Equations of line23 mins
Straight line | Analyse your learning through quiz56 mins
General Equation of a line43 mins
Motion in a Straight Line - 0665 mins
Motion in a Straight Line - 0556 mins
Motion in a Straight Line - 0372 mins
Understand The Interesting Concept Of Relative velocity in 1- Dimension44 mins
By using the concept of slope, show that the points (– 2, – 1), (4, 0), (3, 3) and (– 3, 2) vertices of a parallelogram.
RD Sharma - MathematicsFind the angle between X - axis and the line joining the points (3, – 1) and (4, – 2).
RD Sharma - MathematicsWithout using the distance formula, show that points (– 2, – 1), (4, 0), (3, 3) and (– 3, 2) are the vertices of a parallelogram.
RD Sharma - MathematicsThe equation of the line through the intersection of the lines 2x – 3y = 0 and 4x – 5y = 2 and
The value of the λ, if the lines (2x + 3y + 4) + λ (6x – y + 12) = 0 are
Equation of the line passing through (1, 2) and parallel to the line y = 3x – 1 is
Mathematics - ExemplarThe equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is
Mathematics - Exemplar