हिंदी

If Three Point (H, 0), (A, B) and (0, K) Lie on a Line, Show that Q/H + B/K = 1

Advertisements
Advertisements

प्रश्न

If three point (h, 0), (a, b) and (0, k) lie on a line, show that `q/h + b/k = 1`

Advertisements

उत्तर

If the points A (h, 0), B (a, b), and C (0, k) lie on a line, then

Slope of AB = Slope of BC

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

वीडियो ट्यूटोरियलVIEW ALL [1]

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.


Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).


Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0, –4) and B (8, 0).


Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (–1, –1) are the vertices of a right angled triangle.


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).


Find the equation of a line drawn perpendicular to the line `x/4 + y/6 = 1`through the point, where it meets the y-axis.


Find the value of p so that the three lines 3x + y – 2 = 0, px + 2y – 3 = 0 and 2x – y – 3 = 0 may intersect at one point.


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:

\[(a t_1^2 , 2 a t_1 ) \text { and } (a t_2^2 , 2 a t_2 )\]


Using the method of slope, show that the following points are collinear A (4, 8), B (5, 12), C (9, 28).


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)?


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: \[\frac{a}{h} + \frac{b}{k} = 1\].


The slope of a line is double of the slope of another line. If tangents of the angle between them is \[\frac{1}{3}\],find the slopes of the other line.


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 intersecting the x-axis at a distance of 3 units to the left of origin.


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.


If the image of the point (2, 1) with respect to a line mirror is (5, 2), find the equation of the mirror.


Find the equation of the right bisector of the line segment joining the points (3, 4) and (−1, 2).


Find the angles between the following pair of straight lines:

3x − y + 5 = 0 and x − 3y + 1 = 0


Show that the line a2x + ay + 1 = 0 is perpendicular to the line x − ay = 1 for all non-zero real values of a.


If two opposite vertices of a square are (1, 2) and (5, 8), find the coordinates of its other two vertices and the equations of its sides.


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


Find k, if the slope of one of the lines given by kx2 + 8xy + y2 = 0 exceeds the slope of the other by 6.


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 ______.


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 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 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 ______.


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)`


The coordinates of the foot of perpendiculars from the point (2, 3) on the line y = 3x + 4 is given by ______.


The points (3, 4) and (2, – 6) are situated on the ______ of the line 3x – 4y – 8 = 0.


The equation of the line through the intersection of the lines 2x – 3y = 0 and 4x – 5y = 2 and

Column C1 Column C2
(a) Through the point (2, 1) is (i) 2x – y = 4
(b) Perpendicular to the line (ii) x + y – 5
= 0 x + 2y + 1 = 0 is
(ii) x + y – 5 = 0
(c) Parallel to the line (iii) x – y –1 = 0
3x – 4y + 5 = 0 is
(iii) x – y –1 = 0
(d) Equally inclined to the axes is (iv) 3x – 4y – 1 = 0

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×