Advertisements
Advertisements
Question
If the three points (3, – 1), (a, 3) and (1, – 3) are collinear, find the value of a
Solution
The vertices are A(3, – 1), B(a, 3) and C(1, – 3)
Slope of a line = `(y_2 - y_1)/(x_2 - x_1)`
Slope of AB = `(3 + 1)/("a" - 3) = 4/("a" - 3)`
Slope of BC = `(3 + 3)/("a" - 1) = 6/("a" - 1)`
Since the three points are collinear.
Slope of AB = Slope BC
`4/("a" - 3) = 6/("a" - 1)`
6(a – 3) = 4(a – 1)
6a – 18 = 4a – 4
6a – 4a = – 4 + 18
2a = 14
⇒ a = `14/2` = 7
The value of a = 7
APPEARS IN
RELATED QUESTIONS
What is the inclination of a line whose slope is 1
Find the slope of a line joining the points
`(5, sqrt(5))` with the origin
Find the slope of a line joining the points
(sin θ, – cos θ) and (– sin θ, cos θ)
The line through the points (– 2, a) and (9, 3) has slope `-1/2` Find the value of a.
The line through the points (– 2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x.
Show that the given points form a right angled triangle and check whether they satisfy Pythagoras theorem.
L(0, 5), M(9, 12) and N(3, 14)
If the points A(2, 2), B(– 2, – 3), C(1, – 3) and D(x, y) form a parallelogram then find the value of x and y.
Let A(3, – 4), B(9, – 4), C(5, – 7) and D(7, – 7). Show that ABCD is a trapezium.
The slope of the line joining (12, 3), (4, a) is `1/8`. The value of ‘a’ is
The slope of the line which is perpendicular to a line joining the points (0, 0) and (− 8, 8) is
