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प्रश्न
If (x , 2), (−3, −4) and (7, −5) are collinear, then x =
विकल्प
60
63
−63
−60
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उत्तर
We have three collinear points A (x , 2 ) ; B ( -3 ,-4) ; C(7 , - 5).
In general if A (x1 , y1) ; B (x2 , y2) ; C (x3 , y 3). are collinear then,
`x_1 ( y_2 -y_3) + x_2 (y_3 - y_1) + x_3 (y_1 - y_2 ) = 0`
So,
x (-4 + 5 ) -3 (-5-2)+ 7 (2 +4) = 0
So,
`x + 42 + 21 = 0`
Therefore,
x = - 63
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संबंधित प्रश्न
(Street Plan): A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction.
All the other streets of the city run parallel to these roads and are 200 m apart. There are 5 streets in each direction. Using 1cm = 200 m, draw a model of the city on your notebook. Represent the roads/streets by single lines.
There are many cross- streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East - West direction. Each cross street is referred to in the following manner : If the 2nd street running in the North - South direction and 5th in the East - West direction meet at some crossing, then we will call this cross-street (2, 5). Using this convention, find:
- how many cross - streets can be referred to as (4, 3).
- how many cross - streets can be referred to as (3, 4).
On which axis do the following points lie?
R(−4,0)
Find the value of k, if the point P (0, 2) is equidistant from (3, k) and (k, 5).
Name the quadrilateral formed, if any, by the following points, and given reasons for your answers:
A(-3, 5) B(3, 1), C (0, 3), D(-1, -4)
Find a point on y-axis which is equidistant from the points (5, -2) and (-3, 2).
Three consecutive vertices of a parallelogram are (-2,-1), (1, 0) and (4, 3). Find the fourth vertex.
In what ratio is the line segment joining (-3, -1) and (-8, -9) divided at the point (-5, -21/5)?
Find the ratio in which the line segment joining (-2, -3) and (5, 6) is divided by x-axis Also, find the coordinates of the point of division in each case.
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.
If the point `P (1/2,y)` lies on the line segment joining the points A(3, –5) and B(–7, 9) then find the ratio in which P divides AB. Also, find the value of y.
Points (−4, 0) and (7, 0) lie
The ordinate of any point on x-axis is
If the mid-point of the segment joining A (x, y + 1) and B (x + 1, y + 2) is C \[\left( \frac{3}{2}, \frac{5}{2} \right)\] , find x, y.
What is the distance between the points A (c, 0) and B (0, −c)?
If the points P (x, y) is equidistant from A (5, 1) and B (−1, 5), then
The coordinates of the fourth vertex of the rectangle formed by the points (0, 0), (2, 0), (0, 3) are
Find the point on the y-axis which is equidistant from the points (S, - 2) and (- 3, 2).
Find the coordinates of point A, where AB is a diameter of the circle with centre (–2, 2) and B is the point with coordinates (3, 4).
Point (3, 0) lies in the first quadrant.
In which quadrant, does the abscissa, and ordinate of a point have the same sign?
