Advertisements
Advertisements
प्रश्न
For what values of k are the points (8, 1), (3, –2k) and (k, –5) collinear ?
Advertisements
उत्तर
\[\therefore \frac{1}{2}\left[ 8\left( - 2k + 5 \right) + 3\left( - 5 - 1 \right) + k\left( 1 + 2k \right) \right] = 0\]
\[ \Rightarrow - 16k + 40 - 18 + k + 2 k^2 = 0\]
\[ \Rightarrow 2 k^2 - 15k + 22 = 0\]
\[ \Rightarrow 2 k^2 - 11k - 4k + 22 = 0\]
\[ \Rightarrow k\left( 2k - 11 \right) - 2\left( 2k - 11 \right) = 0\]
\[ \Rightarrow \left( k - 2 \right)\left( 2k - 11 \right) = 0\]
\[ \Rightarrow k - 2 = 0 or 2k - 11 = 0\]
\[ \Rightarrow k = 2 or k = \frac{11}{2}\]
Thus, the values of k are 2 and
\[\frac{11}{2}\]
APPEARS IN
संबंधित प्रश्न
Find the distance between two points
(i) P(–6, 7) and Q(–1, –5)
(ii) R(a + b, a – b) and S(a – b, –a – b)
(iii) `A(at_1^2,2at_1)" and " B(at_2^2,2at_2)`
Show that the points (a, a), (–a, –a) and (– √3 a, √3 a) are the vertices of an equilateral triangle. Also find its area.
If two vertices of an equilateral triangle be (0, 0), (3, √3 ), find the third vertex
Show that the points A (1, −2), B (3, 6), C (5, 10) and D (3, 2) are the vertices of a parallelogram.
Find the distance of the following points from the origin:
(ii) B(-5,5)
Using the distance formula, show that the given points are collinear:
(6, 9), (0, 1) and (-6, -7)
Show that the ▢PQRS formed by P(2, 1), Q(–1, 3), R(–5, –3) and S(–2, –5) is a rectangle.
The distance between points P(–1, 1) and Q(5, –7) is ______
Find distance CD where C(– 3a, a), D(a, – 2a)
Case Study -2
A hockey field is the playing surface for the game of hockey. Historically, the game was played on natural turf (grass) but nowadays it is predominantly played on an artificial turf.
It is rectangular in shape - 100 yards by 60 yards. Goals consist of two upright posts placed equidistant from the centre of the backline, joined at the top by a horizontal crossbar. The inner edges of the posts must be 3.66 metres (4 yards) apart, and the lower edge of the crossbar must be 2.14 metres (7 feet) above the ground.
Each team plays with 11 players on the field during the game including the goalie. Positions you might play include -
- Forward: As shown by players A, B, C and D.
- Midfielders: As shown by players E, F and G.
- Fullbacks: As shown by players H, I and J.
- Goalie: As shown by player K.
Using the picture of a hockey field below, answer the questions that follow:
The point on y axis equidistant from B and C is ______.
