Advertisements
Advertisements
Question
Show that the points (1, 3), (2, 1) and `(1/2, 4)` are collinear, by using concept of slope
Solution
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
RELATED QUESTIONS
Find the slope of the following line which passes through the points:
C(−2, 3), D(5, 7)
Find the slope of the line whose inclination is 30°
A line makes intercepts 3 and 3 on the co-ordinate axes. Find the inclination of the line.
Without using Pythagoras theorem show that points A(4, 4), B(3, 5) and C(−1, −1) are the vertices of a right angled triangle.
If points A(h, 0), B(0, k) and C(a, b) lie on a line then show that `"a"/"h" + "b"/"k"` = 1
Select the correct option from the given alternatives:
If A is (5, −3) and B is a point on the x-axis such that the slope of line AB is −2 then B ≡
Find the equation of the lines passing through the point (1,1) and (– 2, 3)
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)`
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 C for 98.6°F
An object was launched from a place P in constant speed to hit a target. At the 15th second, it was 1400 m from the target, and at the 18th second 800 m away. Find the distance between the place and the target
Find the equation of the line, if the perpendicular drawn from the origin makes an angle 30° with x-axis and its length is 12
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 the bridge of length 850 m
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
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
Find the coordinates of the point which divides the line segment joining the points (1, –2, 3) and (3, 4, –5) internally in the ratio 2 : 3.
The equation of the line passing through the point (–3, 1) and bisecting the angle between co-ordinate axes is ______.
