Advertisements
Advertisements
प्रश्न
State whether the two lines in each of the following is parallel, perpendicular or neither.
Through (3, 15) and (16, 6); through (−5, 3) and (8, 2).
Advertisements
उत्तर
Through (3, 15) and (16, 6); through (−5, 3) and (8, 2).
Let m1 be the slope of the line joining (3, 15) and (16, 6) and m2 be the slope of the line joining (−5, 3) and (8, 2).
\[\therefore m_1 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - 15}{16 - 3} = \frac{- 9}{13} \text { and } m_2 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 3}{8 + 5} = \frac{- 1}{13}\]
\[\text { Now }, m_1 m_2 = \frac{- 9}{13} \times \frac{- 1}{13} = \frac{9}{169}\]
\[\text { Since, } m_1 m_2 \neq - 1 \text { and } m_1 \neq m_2\]
Therefore, the given lines are neither parallel nor perpendicular.
APPEARS IN
संबंधित प्रश्न
The base of an equilateral triangle with side 2a lies along they y-axis such that the mid point of the base is at the origin. Find vertices of the triangle.
Without using distance formula, show that points (–2, –1), (4, 0), (3, 3) and (–3, 2) are vertices of a parallelogram.
If three point (h, 0), (a, b) and (0, k) lie on a line, show that `q/h + b/k = 1`
Using the method of slope, show that the following points are collinear A (4, 8), B (5, 12), C (9, 28).
Using the method of slope, show that the following points are collinear A (16, − 18), B (3, −6), C (−10, 6) .
What can be said regarding a line if its slope is zero ?
What can be said regarding a line if its slope is positive ?
Show that the line joining (2, −3) and (−5, 1) is parallel to the line joining (7, −1) and (0, 3).
Show that the line joining (2, −5) and (−2, 5) is perpendicular to the line joining (6, 3) and (1, 1).
If three points A (h, 0), P (a, b) and B (0, k) lie on a line, show that: \[\frac{a}{h} + \frac{b}{k} = 1\].
Consider the following population and year graph:
Find the slope of the line AB and using it, find what will be the population in the year 2010.
Find the value of x for which the points (x, −1), (2, 1) and (4, 5) are collinear.
By using the concept of slope, show that the points (−2, −1), (4, 0), (3, 3) and (−3, 2) are the vertices of a parallelogram.
Find the equation of a straight line with slope 2 and y-intercept 3 .
Find the equation of a straight line with slope −2 and intersecting the x-axis at a distance of 3 units to the left of origin.
Find the equations of the bisectors of the angles between the coordinate axes.
Find the equation of a line which is perpendicular to the line joining (4, 2) and (3, 5) and cuts off an intercept of length 3 on y-axis.
Find the angles between the following pair of straight lines:
x − 4y = 3 and 6x − y = 11
Find the tangent of the angle between the lines which have intercepts 3, 4 and 1, 8 on the axes respectively.
The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y − 11 = 0 are
The reflection of the point (4, −13) about the line 5x + y + 6 = 0 is
If m1 and m2 are slopes of lines represented by 6x2 - 5xy + y2 = 0, then (m1)3 + (m2)3 = ?
The line passing through (– 2, 0) and (1, 3) makes an angle of ______ with X-axis.
If the line joining two points A(2, 0) and B(3, 1) is rotated about A in anticlock wise direction through an angle of 15°. Find the equation of the line in new position.
Find the equation to the straight line passing through the point of intersection of the lines 5x – 6y – 1 = 0 and 3x + 2y + 5 = 0 and perpendicular to the line 3x – 5y + 11 = 0.
If one diagonal of a square is along the line 8x – 15y = 0 and one of its vertex is at (1, 2), then find the equation of sides of the square passing through this vertex.
The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y – 11 = 0 are ______.
The intercept cut off by a line from y-axis is twice than that from x-axis, and the line passes through the point (1, 2). The equation of the line is ______.
The reflection of the point (4, – 13) about the line 5x + y + 6 = 0 is ______.
Find the angle between the lines y = `(2 - sqrt(3)) (x + 5)` and y = `(2 + sqrt(3))(x - 7)`
Show that the tangent of an angle between the lines `x/a + y/b` = 1 and `x/a - y/b` = 1 is `(2ab)/(a^2 - b^2)`
Find the equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of 120° with the positive direction of x-axis.
Slope of a line which cuts off intercepts of equal lengths on the axes is ______.
Equation of the line passing through (1, 2) and parallel to the line y = 3x – 1 is ______.
The point (4, 1) undergoes the following two successive transformations:
(i) Reflection about the line y = x
(ii) Translation through a distance 2 units along the positive x-axis Then the final coordinates of the point are ______.
The points (3, 4) and (2, – 6) are situated on the ______ of the line 3x – 4y – 8 = 0.
The lines whose vector equations are `r = 2hati - 3hatj + 7hatk + lambda (2hati + phatj + 5hatk) and r = hati - 2hatj + 3hatk + µ(3hati + phatj + phatk)` are perpendicular for all values of λ and µ if p =
