Advertisements
Advertisements
प्रश्न
State whether the two lines in each of the following is parallel, perpendicular or neither.
Through (6, 3) and (1, 1); through (−2, 5) and (2, −5)
Advertisements
उत्तर
Through (6, 3) and (1, 1); through (−2, 5) and (2, −5).
Let m1 be the slope of the line joining (6, 3) and (1, 1) and m2 be the slope of the line joining (−2, 5) and (2, −5).
\[\therefore m_1 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 3}{1 - 6} = \frac{- 2}{- 5} = \frac{2}{5} \text { and } m_2 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{- 5 - 5}{2 + 2} = \frac{- 10}{4} = \frac{- 5}{2}\]
\[\text { Now,} m_1 m_2 = \frac{2}{5} \times \frac{- 5}{2} = - 1\]
\[\text { Since, } m_1 m_2 = - 1\]
Therefore, the given lines are perpendicular.
APPEARS IN
संबंधित प्रश्न
Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).
Find the slope of the line, which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.
Find the value of x for which the points (x, –1), (2, 1) and (4, 5) are collinear.
Find the angle between the x-axis and the line joining the points (3, –1) and (4, –2).
A line passes through (x1, y1) and (h, k). If slope of the line is m, show that k – y1 = m (h – x1).
Find the values of k for which the line (k–3) x – (4 – k2) y + k2 –7k + 6 = 0 is
- Parallel to the x-axis,
- Parallel to the y-axis,
- Passing through the origin.
Find the slope of a line passing through the following point:
(−3, 2) and (1, 4)
State whether the two lines in each of the following are parallel, perpendicular or neither.
Through (5, 6) and (2, 3); through (9, −2) and (6, −5)
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).
Using the method of slope, show that the following points are collinear A (16, − 18), B (3, −6), C (−10, 6) .
Show that the line joining (2, −5) and (−2, 5) is perpendicular to the line joining (6, 3) and (1, 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).
Line through the points (−2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x.
A quadrilateral has vertices (4, 1), (1, 7), (−6, 0) and (−1, −9). Show that the mid-points of the sides of this quadrilateral form a parallelogram.
Find the equations of the straight lines which cut off an intercept 5 from the y-axis and are equally inclined to the axes.
Find the coordinates of the orthocentre of the triangle whose vertices are (−1, 3), (2, −1) and (0, 0).
Find the angles between the following pair of straight lines:
3x + y + 12 = 0 and x + 2y − 1 = 0
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.
Find the angle between the line joining the points (2, 0), (0, 3) and the line x + y = 1.
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 \[\left( \frac{a}{b} \right)\].
Find the tangent of the angle between the lines which have intercepts 3, 4 and 1, 8 on the axes respectively.
Show that the tangent of an angle between the lines \[\frac{x}{a} + \frac{y}{b} = 1 \text { and } \frac{x}{a} - \frac{y}{b} = 1\text { is } \frac{2ab}{a^2 - b^2}\].
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.
If the slope of a line passing through the point A(3, 2) is `3/4`, then find points on the line which are 5 units away from the point A.
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.
The two lines ax + by = c and a′x + b′y = c′ are perpendicular if ______.
The equation of the line passing through (1, 2) and perpendicular to x + y + 7 = 0 is ______.
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.
A variable line passes through a fixed point P. The algebraic sum of the perpendiculars drawn from the points (2, 0), (0, 2) and (1, 1) on the line is zero. Find the coordinates of the point P.
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 ______.
