Advertisements
Advertisements
प्रश्न
Find the value of k for which points P(k, −1), Q(2, 1) and R(4, 5) are collinear.
उत्तर
Given, points P(k, −1), Q(2, 1) and R(4, 5) are collinear.
∴ Slope of PQ = Slope of QR
∴ `(1 - (-1))/(2 - "k") = (5 - 1)/(4 - 2)`
∴ `2/(2 - "k") = 4/2`
∴ 4 = 4 (2 − k)
∴ 1 = 2 − k
∴ k = 2 − 1 = 1
APPEARS IN
संबंधित प्रश्न
Find the slope of the following line which passes through the points:
A(2, −1), B(4, 3)
Find the slope of the following line which passes through the points:
C(−2, 3), D(5, 7)
Find the slope of the following line which passes through the points:
G(7, 1), H(−3, 1)
A line makes intercepts 3 and 3 on the co-ordinate axes. Find the inclination of the line.
Find the slope of the line which makes angle of 45° with the positive direction of the Y-axis measured anticlockwise
Select the correct option from the given alternatives:
A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. Its y−interecpt is
Select the correct option from the given alternatives:
The angle between the line `sqrt(3)x - y - 2` = 0 and `x - sqrt(3)y + 1` = 0 is
Select the correct option from the given alternatives:
If kx + 2y − 1 = 0 and 6x − 4y + 2 = 0 are identical lines, then determine k
Answer the following question:
Find the value of k the point P(1, k) lies on the line passing through the points A(2, 2) and B(3, 3)
Find the equation of the lines passing through the point (1, 1) with y-intercept (– 4)
Find the equation of the lines passing through the point (1,1) with slope 3
Find the equation of the lines passing through the point (1, 1) and the perpendicular from the origin makes an angle 60° with x-axis
Find the equation of the line passing through the point (1, 5) and also divides the co-ordinate axes in the ratio 3:10
If p is length of perpendicular from origin to the line whose intercepts on the axes are a and b, then show that `1/("p"^3) = 1/("a"^2) + 1/("b"^2)`
The normal boiling point of water is 100°C or 212°F and the freezing point of water is 0°C or 32°F. Find the linear relationship between C and F
The normal boiling point of water is 100°C or 212°F and the freezing point of water is 0°C or 32°F. Find the value of F for 38°C
Show that the points (1, 3), (2, 1) and `(1/2, 4)` are collinear, by using a straight line
A 150 m long train is moving with constant velocity of 12.5 m/s. Find time taken to cross a pole
A spring was hung from a hook in the ceiling. A number of different weights were attached to the spring to make it stretch, and the total length of the spring was measured each time is shown in the following table
| Weight (kg) | 2 | 4 | 5 | 8 |
| Length (cm) | 3 | 4 | 4.5 | 6 |
Find the equation relating the length of the spring to the weight on it
A spring was hung from a hook in the ceiling. A number of different weights were attached to the spring to make it stretch, and the total length of the spring was measured each time is shown in the following table
| Weight (kg) | 2 | 4 | 5 | 8 |
| Length (cm) | 3 | 4 | 4.5 | 6 |
What is the actual length of the spring
A spring was hung from a hook in the ceiling. A number of different weights were attached to the spring to make it stretch, and the total length of the spring was measured each time is shown in the following table
| Weight (kg) | 2 | 4 | 5 | 8 |
| Length (cm) | 3 | 4 | 4.5 | 6 |
How long will the spring be when 6 kilograms of weight on it?
A family is using Liquefied petroleum gas (LPG) of weight 14.2 kg for consumption. (Full weight 29.5kg includes the empty cylinders tare weight of 15.3kg.). If it is used with constant rate then it lasts for 24 days. Then the new cylinder is replaced. Find the equation relating the quantity of gas in the cylinder to the days
In a shopping mall there is a hall of cuboid shape with dimension 800 × 800 × 720 units, which needs to be added the facility of an escalator in the path as shown by the dotted line in the figure. Find the heights at which the escalator changes its direction
Choose the correct alternative:
Equation of the straight line perpendicular to the line x − y + 5 = 0, through the point of intersection the y-axis and the given line
Choose the correct alternative:
The line (p + 2q)x + (p − 3q)y = p − q for different values of p and q passes through the point
If one of the lines given by kx2 + 2xy – 3y2 = 0 is perpendicular to the line 3x + 5y+ 1 = 0, then the value of k is ______.
The number of possible tangents which can be drawn to the curve 4x2 – 9y2 = 36, which are perpendicular to the straight line 5x + 2y – 10 = 0 is ______.
The coordinates of vertices of base BC of an isosceles triangle ABC are given by B(1, 3) and C(–2, 7) which of the following points can be the possible coordinates of the vertex A?
The equation of the line passing through the point (–3, 1) and bisecting the angle between co-ordinate axes is ______.
If planes x – cy – bz = 0, cx – y + az = 0 and bx + ay – z = 0 pass through a straight line then a2 + b2 + c2 = ______.
Find the transformed equation of the straight line 2x – 3y + 5 = 0, when the origin is shifted to the point (3, –1) after translation of axes.
