Advertisements
Advertisements
प्रश्न
Find the angles between the following pair of straight lines:
3x + 4y − 7 = 0 and 4x − 3y + 5 = 0
उत्तर
The equations of the lines are
3x + 4y − 7 = 0 ... (1)
4x − 3y + 5 = 0 ... (2)
Let \[m_1 \text { and } m_2\] be the slopes of these lines.
\[m_1 = - \frac{3}{4}, m_2 = \frac{4}{3}\]
\[\because m_1 m_2 = - \frac{3}{4} \times \frac{4}{3}\]
\[ = - 1\]
Hence, the given lines are perpendicular.
Therefore, the angle between them is 90°.
APPEARS IN
संबंधित प्रश्न
Without using distance formula, show that points (–2, –1), (4, 0), (3, 3) and (–3, 2) are vertices of a parallelogram.
Find the slope of the lines which make the following angle with the positive direction of x-axis:
\[\frac{2\pi}{3}\]
Find the slope of a line passing through the following point:
(−3, 2) and (1, 4)
Find the slope of a line passing through the following point:
(3, −5), and (1, 2)
Using the method of slope, show that the following points are collinear A (16, − 18), B (3, −6), C (−10, 6) .
What is the value of y so that the line through (3, y) and (2, 7) is parallel to the line through (−1, 4) and (0, 6)?
Prove that the points (−4, −1), (−2, −4), (4, 0) and (2, 3) are the vertices of a rectangle.
If three points A (h, 0), P (a, b) and B (0, k) lie on a line, show that: \[\frac{a}{h} + \frac{b}{k} = 1\].
Without using the distance formula, show that points (−2, −1), (4, 0), (3, 3) and (−3, 2) are the vertices of a parallelogram.
Find the angle between the X-axis and the line joining the points (3, −1) and (4, −2).
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 line which is perpendicular to the line joining (4, 2) and (3, 5) and cuts off an intercept of length 3 on y-axis.
Show that the perpendicular bisectors of the sides of a triangle are concurrent.
Find the equations of the altitudes of a ∆ ABC whose vertices are A (1, 4), B (−3, 2) and C (−5, −3).
The line through (h, 3) and (4, 1) intersects the line 7x − 9y − 19 = 0 at right angle. Find the value of h.
Find the angles between the following pair of straight lines:
3x − y + 5 = 0 and x − 3y + 1 = 0
Find the angles between the following pair of straight lines:
x − 4y = 3 and 6x − y = 11
Prove that the points (2, −1), (0, 2), (2, 3) and (4, 0) are the coordinates of the vertices of a parallelogram and find the angle between its diagonals.
Prove that the straight lines (a + b) x + (a − b ) y = 2ab, (a − b) x + (a + b) y = 2ab and x + y = 0 form an isosceles triangle whose vertical angle is 2 tan−1 \[\left( \frac{a}{b} \right)\].
Show that the tangent of an angle between the lines \[\frac{x}{a} + \frac{y}{b} = 1 \text { and } \frac{x}{a} - \frac{y}{b} = 1\text { is } \frac{2ab}{a^2 - b^2}\].
Write the coordinates of the image of the point (3, 8) in the line x + 3y − 7 = 0.
The equation of the line with slope −3/2 and which is concurrent with the lines 4x + 3y − 7 = 0 and 8x + 5y − 1 = 0 is
The equation of a line passing through the point (7, - 4) and perpendicular to the line passing through the points (2, 3) and (1 , - 2 ) is ______.
Find the equation of the straight line passing through (1, 2) and perpendicular to the line x + y + 7 = 0.
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.
A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and then passes through the point (5, 3). Find the coordinates of the point A.
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 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 ______.
Find the equation of the line passing through the point (5, 2) and perpendicular to the line joining the points (2, 3) and (3, – 1).
Find the equation of one of the sides of an isosceles right angled triangle whose hypotenuse is given by 3x + 4y = 4 and the opposite vertex of the hypotenuse is (2, 2).
If the equation of the base of an equilateral triangle is x + y = 2 and the vertex is (2, – 1), then find the length of the side of the triangle.
The coordinates of the foot of perpendiculars from the point (2, 3) on the line y = 3x + 4 is given by ______.
Equations of the lines through the point (3, 2) and making an angle of 45° with the line x – 2y = 3 are ______.
If the vertices of a triangle have integral coordinates, then the triangle can not be equilateral.
The points A(– 2, 1), B(0, 5), C(– 1, 2) are collinear.
Line joining the points (3, – 4) and (– 2, 6) is perpendicular to the line joining the points (–3, 6) and (9, –18).
