Advertisements
Advertisements
Question
Determine whether the given set of points are collinear or not
(7, −2), (5, 1), (3, 4)
Advertisements
Solution
To prove that three points are collinear, sum of the distance between two pairs of points is equal to the third pair of points.
Distance AB = `sqrt((5 - 7)^2 + (1 + 2)^2`
= `sqrt((-2)^2 + (3)^2`
= `sqrt(4 + 9)`
= `sqrt(13)`
BC = `sqrt((3 - 5)^2 + (4 - 1)^2`
= `sqrt((-2)^2 + (3)^2`
= `sqrt(4 + 9)`
= `sqrt(13)`
AC = `sqrt((3 - 7)^2 + (4 + 2)^2`
= `sqrt((-4)^2 + (6)^2`
= `sqrt(16 + 36)`
= `sqrt(52)`
= `sqrt(2 xx 2 xx 13)`
= `2sqrt(13)`
AB + BC = AC
`sqrt(13) + sqrt(13) = 2sqrt(13)`
⇒ `2sqrt(13) = 2sqrt(13)`
∴ The given three points are collinear.
APPEARS IN
RELATED QUESTIONS
Find the distance with the help of the number line given below.
d (Q, B)
If the co-ordinate of A is x and that of B is y, find d(A, B).
x = 1, y = 7
If the co-ordinate of A is x and that of B is y, find d(A, B).
x = -4, y = -5
Co-ordinates of the pair of points are given below. Hence find the distance between the pair.
0, - 2
Co-ordinates of the pair of points are given below. Hence find the distance between the pair.
- 25, - 47
Co-ordinates of the pair of points are given below. Hence find the distance between the pair.
80, - 85
Show that the following points taken in order to form an isosceles triangle
A(5, 4), B(2, 0), C(−2, 3)
Show that the point (11, 2) is the centre of the circle passing through the points (1, 2), (3, −4) and (5, −6)
If (x + 2, 4) = (5, y – 2), then the coordinates (x, y) are _____
Find the distance with the help of the number line given below.
d(P, C)
