Advertisements
Advertisements
Question
If the points (k, 2k), (3k, 3k) and (3, 1) are collinear, then k
Options
- \[\frac{1}{3}\]
- \[- \frac{1}{3}\]
- \[\frac{2}{3}\]
- \[- \frac{2}{3}\]
Advertisements
Solution
We have three collinear points A(k, 2k) : B(3k, 3k) : C (3, 1) .
In general if `A(x_1 , y_1) ; B (x_2 ,y_2) ; C(x_3 ,y_3) `are collinear then, area of the triangle is 0.
`x_1 (y_2 - y_3 ) + x_2 (y_3 - y_1) + x_3 (y_1- y_2 ) = 0`
So,
`k (3k - 1 ) + 3k(1 - 2k) + 3 (2k - 3k) = 0`
So,
-3k2 - k = 0
Take out the common terms,
-k (3k + 1) = 0
Therefore,
`k = -1/3`
APPEARS IN
RELATED QUESTIONS
On which axis do the following points lie?
S(0,5)
Find the value of x such that PQ = QR where the coordinates of P, Q and R are (6, -1), (1, 3) and (x, 8) respectively.
The line segment joining the points P(3, 3) and Q(6, -6) is trisected at the points A and B such that Ais nearer to P. If A also lies on the line given by 2x + y + k = 0, find the value of k.
In what ratio is the line segment joining the points A(-2, -3) and B(3,7) divided by the yaxis? Also, find the coordinates of the point of division.
Find the point on x-axis which is equidistant from points A(-1,0) and B(5,0)
Find the area of the quadrilateral ABCD, whose vertices are A(−3, −1), B (−2, −4), C(4, − 1) and D (3, 4).
The measure of the angle between the coordinate axes is
The ordinate of any point on x-axis is
The abscissa of a point is positive in the
Find the value of k, if the points A(7, −2), B (5, 1) and C (3, 2k) are collinear.
Find the value of a for which the area of the triangle formed by the points A(a, 2a), B(−2, 6) and C(3, 1) is 10 square units.
Write the perimeter of the triangle formed by the points O (0, 0), A (a, 0) and B (0, b).
The distance between the points (cos θ, 0) and (sin θ − cos θ) is
If (x , 2), (−3, −4) and (7, −5) are collinear, then x =
If points (a, 0), (0, b) and (1, 1) are collinear, then \[\frac{1}{a} + \frac{1}{b} =\]
The coordinates of the point P dividing the line segment joining the points A (1, 3) and B(4, 6) in the ratio 2 : 1 are
Which of the points P(-1, 1), Q(3, - 4), R(1, -1), S (-2, -3), T(-4, 4) lie in the fourth quadrant?
In the above figure, seg PA, seg QB and RC are perpendicular to seg AC. From the information given in the figure, prove that: `1/x + 1/y = 1/z`
What are the coordinates of origin?
A tiling or tessellation of a flat surface is the covering of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. Historically, tessellations were used in ancient Rome and in Islamic art. You may find tessellation patterns on floors, walls, paintings etc. Shown below is a tiled floor in the archaeological Museum of Seville, made using squares, triangles and hexagons.
A craftsman thought of making a floor pattern after being inspired by the above design. To ensure accuracy in his work, he made the pattern on the Cartesian plane. He used regular octagons, squares and triangles for his floor tessellation pattern
Use the above figure to answer the questions that follow:
- What is the length of the line segment joining points B and F?
- The centre ‘Z’ of the figure will be the point of intersection of the diagonals of quadrilateral WXOP. Then what are the coordinates of Z?
- What are the coordinates of the point on y-axis equidistant from A and G?
OR
What is the area of Trapezium AFGH?
