Advertisements
Advertisements
प्रश्न
Determine if the points (1, 5), (2, 3) and (−2, −11) are collinear.
Advertisements
उत्तर
Let the points (1, 5), (2, 3), and (−2, −11) be representing the vertices A, B, and C of the given triangle respectively.
Let A = (1,5), B = (2, 3), C = (-2, -11)
∴ `"AB" = sqrt((1-2)^2+(5-3)^2)`
`"BC" = sqrt((2-(-2))^2 + (3-(-11))^2)`
= `sqrt(4^2+14^2)`
= `sqrt(16+196)`
= `sqrt(212)`
= `2sqrt53`
CA = `sqrt((1-(-2))^2 + (5-(-11))^2)`
= `sqrt(3^2+16^2)`
= `sqrt(9+256)`
= `sqrt(265)`
Since AB + BC ≠ CA
Therefore, the points (1, 5), (2, 3), and (−2, −11) are not collinear.
APPEARS IN
संबंधित प्रश्न
Find the distance between two points
(i) P(–6, 7) and Q(–1, –5)
(ii) R(a + b, a – b) and S(a – b, –a – b)
(iii) `A(at_1^2,2at_1)" and " B(at_2^2,2at_2)`
Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:
(−3, 5), (3, 1), (0, 3), (−1, −4)
Show that the points A (1, −2), B (3, 6), C (5, 10) and D (3, 2) are the vertices of a parallelogram.
Given a triangle ABC in which A = (4, −4), B = (0, 5) and C = (5, 10). A point P lies on BC such that BP : PC = 3 : 2. Find the length of line segment AP.
Find the co-ordinates of points of trisection of the line segment joining the point (6, –9) and the origin.
Using the distance formula, show that the given points are collinear:
(6, 9), (0, 1) and (-6, -7)
Using the distance formula, show that the given points are collinear:
(-2, 5), (0,1) and (2, -3)
Determine whether the points are collinear.
L(–2, 3), M(1, –3), N(5, 4)
Determine whether the points are collinear.
P(–2, 3), Q(1, 2), R(4, 1)
Find the distances between the following point.
A(a, 0), B(0, a)
If A and B are the points (−6, 7) and (−1, −5) respectively, then the distance
2AB is equal to
Find the distance between the following point :
(sec θ , tan θ) and (- tan θ , sec θ)
Prove that the points (6 , -1) , (5 , 8) and (1 , 3) are the vertices of an isosceles triangle.
Find the distance between the following pair of points:
`(sqrt(3)+1,1)` and `(0, sqrt(3))`
Calculate the distance between the points P (2, 2) and Q (5, 4) correct to three significant figures.
Give the relation that must exist between x and y so that (x, y) is equidistant from (6, -1) and (2, 3).
If the length of the segment joining point L(x, 7) and point M(1, 15) is 10 cm, then the value of x is ______
Find distance CD where C(– 3a, a), D(a, – 2a)
Using distance formula decide whether the points (4, 3), (5, 1), and (1, 9) are collinear or not.
If the distance between the points (4, P) and (1, 0) is 5, then the value of p is ______.
