Advertisements
Advertisements
Question
If three point (h, 0), (a, b) and (0, k) lie on a line, show that `q/h + b/k = 1`
Advertisements
Solution
If the points A (h, 0), B (a, b), and C (0, k) lie on a line, then
Slope of AB = Slope of BC

APPEARS IN
RELATED QUESTIONS
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).
Find the value of x for which the points (x, –1), (2, 1) and (4, 5) are collinear.
Consider the given 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 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 equation of the lines through the point (3, 2) which make an angle of 45° with the line x –2y = 3.
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 the lines which make the following angle with the positive direction of x-axis: \[\frac{\pi}{3}\]
Find the slope of a line (i) which bisects the first quadrant angle (ii) which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.
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)?
What can be said regarding a line if its slope is negative?
Show that the line joining (2, −5) and (−2, 5) is perpendicular to the line joining (6, 3) and (1, 1).
Find the value of x for which the points (x, −1), (2, 1) and (4, 5) are collinear.
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 equations of the straight lines which cut off an intercept 5 from the y-axis and are equally inclined to the axes.
Find the equations of the altitudes of a ∆ ABC whose vertices are A (1, 4), B (−3, 2) and C (−5, −3).
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 angles between the following pair of straight lines:
3x − y + 5 = 0 and x − 3y + 1 = 0
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 reflection of the point (4, −13) about the line 5x + y + 6 = 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.
If the slopes of the lines given by the equation ax2 + 2hxy + by2 = 0 are in the ratio 5 : 3, then the ratio h2 : ab = ______.
The line passing through (– 2, 0) and (1, 3) makes an angle of ______ with X-axis.
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 equation of the line passing through (1, 2) and perpendicular to x + y + 7 = 0 is ______.
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 ______.
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)`
Equations of diagonals of the square formed by the lines x = 0, y = 0, x = 1 and y = 1 are ______.
One vertex of the equilateral triangle with centroid at the origin and one side as x + y – 2 = 0 is ______.
If the vertices of a triangle have integral coordinates, then the triangle can not be equilateral.
The line `x/a + y/b` = 1 moves in such a way that `1/a^2 + 1/b^2 = 1/c^2`, where c is a constant. The locus of the foot of the perpendicular from the origin on the given line is x2 + y2 = c2.
| Column C1 | Column C2 |
| (a) The coordinates of the points P and Q on the line x + 5y = 13 which are at a distance of 2 units from the line 12x – 5y + 26 = 0 are |
(i) (3, 1), (–7, 11) |
| (b) The coordinates of the point on the line x + y = 4, which are at a unit distance from the line 4x + 3y – 10 = 0 are |
(ii) `(- 1/3, 11/3), (4/3, 7/3)` |
| (c) The coordinates of the point on the line joining A (–2, 5) and B (3, 1) such that AP = PQ = QB are |
(iii) `(1, 12/5), (-3, 16/5)` |
The three straight lines ax + by = c, bx + cy = a and cx + ay = b are collinear, if ______.
