Advertisements
Advertisements
प्रश्न
If the points A (2,3), B (4,k ) and C (6,-3) are collinear, find the value of k.
Advertisements
उत्तर
The given points are A (2,3), B (4,k ) and C (6,-3)
`Here , (x_1 = 2 , y_1 =3) , (x_2 =4, y_2 =k) and (x_3 = 6, y_3=-3)`
It is given that the points A, B and C are collinear. Then,
`x_1(y_2 -y_3 )+x_2 (y_3-y_1)+x_3 (y_1-y_2)=0`
⇒ 2 (k+3) + 4 (-3-3) + 6 (3-k) = 0
⇒ 2k + 6 - 24 +18 -6k =0
⇒ - 4k = 0
⇒ k =0
APPEARS IN
संबंधित प्रश्न
The points (3, -4) and (-6, 2) are the extremities of a diagonal of a parallelogram. If the third vertex is (-1, -3). Find the coordinates of the fourth vertex.
Point A lies on the line segment PQ joining P(6, -6) and Q(-4, -1) in such a way that `(PA)/( PQ)=2/5` . If that point A also lies on the line 3x + k( y + 1 ) = 0, find the value of k.
If (2, p) is the midpoint of the line segment joining the points A(6, -5) and B(-2,11) find the value of p.
In what ratio does the line x - y - 2 = 0 divide the line segment joining the points A (3, 1) and B (8, 9)?
If the point A(0,2) is equidistant from the points B(3,p) and C(p, 5), find p.
The co-ordinates of point A and B are 4 and -8 respectively. Find d(A, B).
Mark the correct alternative in each of the following:
The point of intersect of the coordinate axes is
The abscissa of a point is positive in the
If P ( 9a -2 , - b) divides the line segment joining A (3a + 1 , - 3 ) and B (8a, 5) in the ratio 3 : 1 , find the values of a and b .
Points P, Q, R and S divides the line segment joining A(1, 2) and B(6, 7) in 5 equal parts. Find the coordinates of the points P, Q and R.
If the point \[C \left( - 1, 2 \right)\] divides internally the line segment joining the points A (2, 5) and B( x, y ) in the ratio 3 : 4 , find the value of x2 + y2 .
Find the centroid of the triangle whose vertices is (−2, 3) (2, −1) (4, 0) .
If R (x, y) is a point on the line segment joining the points P (a, b) and Q (b, a), then prove that x + y = a + b.
If the points A(−2, 1), B(a, b) and C(4, −1) ae collinear and a − b = 1, find the values of aand b.
Find the distance between the points \[\left( - \frac{8}{5}, 2 \right)\] and \[\left( \frac{2}{5}, 2 \right)\] .
Which of the points P(-1, 1), Q(3, - 4), R(1, -1), S (-2, -3), T(-4, 4) lie in the fourth quadrant?
Points (1, – 1), (2, – 2), (4, – 5), (– 3, – 4) ______.
If the coordinates of the two points are P(–2, 3) and Q(–3, 5), then (abscissa of P) – (abscissa of Q) is ______.
The point whose ordinate is 4 and which lies on y-axis is ______.
