Advertisements
Advertisements
प्रश्न
Show that the points (1, 3), (2, 1) and `(1/2, 4)` are collinear, by using concept of slope
Advertisements
उत्तर
Let the given points be A(1 , 3), B(2 , 1) and `"C"(1/2, 4)`
Slope Method:
A (1 , 3 ), B (2 , 1 ), `"C"(1/2, 4)`
Slope of AB = `(1 - 3)/(2 - 1)`
= `(-2)/1`
= – 2 .......(1)
Slope of BC = ``(4 - 1)/(1/2 - 2)`
= `3/((1 - 4)/2)`
= `3/((-3)/2)`
= – 2 .......(2)
From equations (1) and (2)
Slope of AB = Slope of BC
∴ The given points A, B, C are collinear.
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)
A line makes intercepts 3 and 3 on the co-ordinate axes. Find the inclination of the line.
Find the acute angle between the X-axis and the line joining points A(3, −1) and B(4, −2).
Answer the following question:
Find the value of k if the slope of the line passing through the points P(3, 4), Q(5, k) is 9
Answer the following question:
Find the value of k the points A(1, 3), B(4, 1), C(3, k) are collinear
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 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
Show that the points (1, 3), (2, 1) and `(1/2, 4)` are collinear, by using any other method
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 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
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. Draw the graph for first 96days
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
Choose the correct alternative:
Straight line joining the points (2, 3) and (−1, 4) passes through the point (α, β) if
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 ______.
