Advertisements
Advertisements
प्रश्न
Using the distance formula, show that the given points are collinear:
(6, 9), (0, 1) and (-6, -7)
Advertisements
उत्तर
Let A( 6,9) ,B( 0,1 ) and C (-6, -7) be the give points. Then
`AB = sqrt((0-6)^2 +(1-9)^2 )= sqrt((-6)^2 +(-8)^2) = sqrt(36 + 64)= sqrt(100)`=10 units
`BC=sqrt((-6-0)^2+(-7-1)^2) = sqrt((-6)^2+(-8)^2)= sqrt(36 + 64)= sqrt(100) `=10 units
`AC = sqrt((-6-6)^2 +(-7-9)^2 )= sqrt((-12)^2 +(16)^2) = sqrt(144 + 256 )= sqrt(400)`= 20 units
∴ AB + BC = (10+10) units - 20 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.
Show that four points (0, – 1), (6, 7), (–2, 3) and (8, 3) are the vertices of a rectangle. Also, find its area
Prove that the points (–3, 0), (1, –3) and (4, 1) are the vertices of an isosceles right angled triangle. Find the area of this triangle
If P (2, – 1), Q(3, 4), R(–2, 3) and S(–3, –2) be four points in a plane, show that PQRS is a rhombus but not a square. Find the area of the rhombus
If a≠b≠0, prove that the points (a, a2), (b, b2) (0, 0) will not be collinear.
Show that the quadrilateral whose vertices are (2, −1), (3, 4) (−2, 3) and (−3,−2) is a rhombus.
A(–8, 0), B(0, 16) and C(0, 0) are the vertices of a triangle ABC. Point P lies on AB and Q lies on AC such that AP : PB = 3 : 5 and AQ : QC = 3 : 5. Show that : PQ = `3/8` BC.
Find the distance of the following point from the origin :
(0 , 11)
Find the distance of a point (7 , 5) from another point on the x - axis whose abscissa is -5.
Find the relation between x and y if the point M (x,y) is equidistant from R (0,9) and T (14 , 11).
Show that the points (2, 0), (–2, 0), and (0, 2) are the vertices of a triangle. Also, a state with the reason for the type of triangle.
Find the distance between the points (a, b) and (−a, −b).
Find the distance between the origin and the point:
(-8, 6)
Point P (2, -7) is the center of a circle with radius 13 unit, PT is perpendicular to chord AB and T = (-2, -4); calculate the length of: AT
The distance between points P(–1, 1) and Q(5, –7) is ______
Using distance formula decide whether the points (4, 3), (5, 1), and (1, 9) are collinear or not.
If the distance between the points (x, -1) and (3, 2) is 5, then the value of x is ______.
The equation of the perpendicular bisector of line segment joining points A(4,5) and B(-2,3) is ______.
Show that points A(–1, –1), B(0, 1), C(1, 3) are collinear.
The distance of the point (5, 0) from the origin is ______.
