Advertisements
Advertisements
प्रश्न
Show that the points (1, 3), (2, 1) and `(1/2, 4)` are collinear, by using a straight line
उत्तर
Let the given points be A (1 , 3), B (2 , 1) and `"C"(1/2, 4)`
Using a straight line
A(1, 3), B(2, 1), `"C"(1/2, 4)`
The equation of the straight line joining the points
A(1, 3), B(2, 1) is
`(x - 1)/(2 - 1) = (y - 3)/(1 - 3)`
`(x - 1)/1 = (y - 3)/(- 2)`
– 2(x – 1) = y – 3
– 2x + 2 = y – 3
2x + y – 2 – 3 = 0
2x + y – 5 = 0 .......(2)
Substituting the third point `"C"(1/2, 4)` in equation (2)
We have `2(1/2) + 4 - 5` = 0
1 + 4 – 5 = 0
0 = 0
∴ The third point `"C"(1/2, 4)` lies on the straight line AB.
Hence the points A, B, C are collinear.
APPEARS IN
संबंधित प्रश्न
If the X and Y-intercepts of lines L are 2 and 3 respectively then find the slope of line L.
Find the slope of the line whose inclination is 30°
Find the slope of the line whose inclination is `pi/4`
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
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)
Answer the following question:
Line through A(h, 3) and B(4, 1) intersect the line 7x − 9y − 19 = 0 at right angle Find the value of h
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
If P(r, c) is midpoint of a line segment between the axes then show that `x/"r" + y/"c"` = 2
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)`
Show that the points (1, 3), (2, 1) and `(1/2, 4)` are collinear, by using concept of slope
A straight line is passing through the point A(1, 2) with slope `5/12`. Find points on the line which are 13 units away from A
A 150 m long train is moving with constant velocity of 12.5 m/s. Find the equation of the motion of the train
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 |
If the spring has to stretch to 9 cm long, how much weight should be added?
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 minimum total length of the escalator
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:
The line (p + 2q)x + (p − 3q)y = p − q for different values of p and q passes through the point
Choose the correct alternative:
The y-intercept of the straight line passing through (1, 3) and perpendicular to 2x − 3y + 1 = 0 is
The distance of the origin from the centroid of the triangle whose two sides have the equations. x – 2y + 1 = 0 and 2x – y – 1 = 0 and whose orthocenter is `(7/3. 7/3)` is ______.
