Advertisements
Advertisements
प्रश्न
Determine whether the given set of points are collinear or not
(7, −2), (5, 1), (3, 4)
Advertisements
उत्तर
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
संबंधित प्रश्न
Sketch proper figure and write the answer of the following question.
If R-S-T and l(ST) = 3.7, l(RS) = 2.5, then l(RT) = ?
On a number line, co-ordinates of P, Q, R are 3, -5 and 6 respectively. State with reason whether the following statement is true or false.
d(P, Q) + d(Q, R) = d(P, R)
On a number line, the co-ordinates of P, Q, R are 3, -5 and 6 respectively. State with reason whether the following statement is true or false.
d(R, P) + d(P, Q) = d(R, Q)
Co-ordinates of the pair of points are given below. Hence find the distance between the pair.
- 25, - 47
Co-ordinate of point P on a number line is - 7. Find the co-ordinates of points on the number line which are at a distance of 8 units from point P.
Show that the following points taken in order to form the vertices of a parallelogram
A(−3, 1), B(−6, −7), C(3, −9) and D(6, −1)
A(−1, 1), B(1, 3) and C(3, a) are point and if AB = BC, then find ‘a’
Show that the point (11, 2) is the centre of the circle passing through the points (1, 2), (3, −4) and (5, −6)
Find the distance with the help of the number line given below.
d(J, A)
Find the distance with the help of the number line given below.
d(O, E)
