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
Find a point on the x-axis which is equidistant from the points (7, 6) and (−3, 4).
A (3, 2) and B (−2, 1) are two vertices of a triangle ABC whose centroid G has the coordinates `(5/3,-1/3)`Find the coordinates of the third vertex C of the triangle.
Prove that (4, 3), (6, 4) (5, 6) and (3, 5) are the angular points of a square.
Find the points on the y-axis which is equidistant form the points A(6,5) and B(- 4,3)
Points P, Q, R and S divide the line segment joining the points A(1,2) and B(6,7) in five equal parts. Find the coordinates of the points P,Q and R
In what ratio does the point P(2,5) divide the join of A (8,2) and B(-6, 9)?
In what ratio is the line segment joining A(2, -3) and B(5, 6) divide by the x-axis? Also, find the coordinates of the pint of division.
Find the area of the quadrilateral ABCD, whose vertices are A(−3, −1), B (−2, −4), C(4, − 1) and D (3, 4).
The ordinate of any point on x-axis is
If A(3, y) is equidistant from points P(8, −3) and Q(7, 6), find the value of y and find the distance AQ.
If (0, −3) and (0, 3) are the two vertices of an equilateral triangle, find the coordinates of its third vertex.
Find the centroid of the triangle whose vertices is (−2, 3) (2, −1) (4, 0) .
Write the perimeter of the triangle formed by the points O (0, 0), A (a, 0) and B (0, b).
what is the value of \[\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab}\] .
If A (1, 2) B (4, 3) and C (6, 6) are the three vertices of a parallelogram ABCD, find the coordinates of fourth vertex D.
Find the area of triangle with vertices ( a, b+c) , (b, c+a) and (c, a+b).
If the points A (1,2) , O (0,0) and C (a,b) are collinear , then find a : b.
f the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (−2, 5), then the coordinates of the other end of the diameter are
What is the form of co-ordinates of a point on the X-axis?
Students of a school are standing in rows and columns in their playground for a drill practice. A, B, C and D are the positions of four students as shown in figure. Is it possible to place Jaspal in the drill in such a way that he is equidistant from each of the four students A, B, C and D? If so, what should be his position?
