Advertisements
Advertisements
प्रश्न
Using the distance formula, show that the given points are collinear:
(-1, -1), (2, 3) and (8, 11)
उत्तर
Let A(-1, -1) , B(2,3) and C( 8,11) be the give points. Then
`AB = sqrt((2+1)^2 +(3+1)^2) = sqrt((3)^2 +(4)^2) = sqrt(25)` =5 units
`BC=sqrt((8-2)^2 +(11-3)^2 = sqrt(6)^2 +(8)^2 = sqrt(100) `= 10 units
`AC = sqrt(( 8+1)^2 +(11+1)^2 ) = sqrt((9)^2 +(12)^2 = sqrt(225) `= 15 units
∴ AB +BC = (5+10) units = 15 units = Ac
Hence, the given points are collinear
APPEARS IN
संबंधित प्रश्न
The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from Q(2, –5) and R(–3, 6), find the coordinates of P.
Find the distance of the following points from the origin:
(ii) B(-5,5)
Using the distance formula, show that the given points are collinear:
(6, 9), (0, 1) and (-6, -7)
Find the distances between the following point.
R(–3a, a), S(a, –2a)
Find the distance of a point (13 , -9) from another point on the line y = 0 whose abscissa is 1.
ABC is an equilateral triangle . If the coordinates of A and B are (1 , 1) and (- 1 , -1) , find the coordinates of C.
Find the distance between the origin and the point:
(8, -15)
By using the distance formula prove that each of the following sets of points are the vertices of a right angled triangle.
(i) (6, 2), (3, -1) and (- 2, 4)
(ii) (-2, 2), (8, -2) and (-4, -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 ______
A circle drawn with origin as the centre passes through `(13/2, 0)`. The point which does not lie in the interior of the circle is ______.
