Advertisements
Advertisements
प्रश्न
If the points A (2,3), B (4,k ) and C (6,-3) are collinear, find the value of k.
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
A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, –5) is the mid-point of PQ, then find the coordinates of P and Q.
If the points A (a, -11), B (5, b), C (2, 15) and D (1, 1) are the vertices of a parallelogram ABCD, find the values of a and b.
Show that the following points are the vertices of a square:
A (6,2), B(2,1), C(1,5) and D(5,6)
Show that the following points are the vertices of a rectangle
A (0,-4), B(6,2), C(3,5) and D(-3,-1)
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.
ABCD is rectangle formed by the points A(-1, -1), B(-1, 4), C(5, 4) and D(5, -1). If P,Q,R and S be the midpoints of AB, BC, CD and DA respectively, Show that PQRS is a rhombus.
The abscissa and ordinate of the origin are
Points (−4, 0) and (7, 0) lie
The area of the triangle formed by the points P (0, 1), Q (0, 5) and R (3, 4) is
If the vertices of a triangle are (1, −3), (4, p) and (−9, 7) and its area is 15 sq. units, find the value(s) of p.
Two vertices of a triangle have coordinates (−8, 7) and (9, 4) . If the centroid of the triangle is at the origin, what are the coordinates of the third vertex?
Find the area of triangle with vertices ( a, b+c) , (b, c+a) and (c, a+b).
The perimeter of the triangle formed by the points (0, 0), (0, 1) and (0, 1) is
The distance of the point (4, 7) from the y-axis is
If P is a point on x-axis such that its distance from the origin is 3 units, then the coordinates of a point Q on OY such that OP = OQ, are
The coordinates of a point on x-axis which lies on the perpendicular bisector of the line segment joining the points (7, 6) and (−3, 4) are
Find the point on the y-axis which is equidistant from the points (S, - 2) and (- 3, 2).
If segment AB is parallel Y-axis and coordinates of A are (1, 3), then the coordinates of B are ______
The coordinates of a point whose ordinate is `-1/2` and abscissa is 1 are `-1/2, 1`.
If the points P(1, 2), Q(0, 0) and R(x, y) are collinear, then find the relation between x and y.
Given points are P(1, 2), Q(0, 0) and R(x, y).
The given points are collinear, so the area of the triangle formed by them is `square`.
∴ `1/2 |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| = square`
`1/2 |1(square) + 0(square) + x(square)| = square`
`square + square + square` = 0
`square + square` = 0
`square = square`
Hence, the relation between x and y is `square`.
