Advertisements
Advertisements
प्रश्न
If Points (1, 2) (−5, 6) and (a, −2) are collinear, then a =
विकल्प
−3
7
2
-2
Advertisements
उत्तर
We have three collinear points A(1,2) ;B(-5,6) ;C(a, - 2).
In general if `A(x_1 ,y_1) ;B(x_2 , y_2) ;C(x_3 ,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,
1(6 + 2) - 5(- 2-2)+ a (2 -6 ) = 0
So,
-4a + 8 + 20 = 0
Therefore,
a = 7
APPEARS IN
संबंधित प्रश्न
Find the point on x-axis which is equidistant from the points (−2, 5) and (2,−3).
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.
Determine the ratio in which the point P (m, 6) divides the join of A(−4, 3) and B(2, 8). Also, find the value of m.
Find the co-ordinates of the point equidistant from three given points A(5,3), B(5, -5) and C(1,- 5).
In what ratio does the point P(2,5) divide the join of A (8,2) and B(-6, 9)?
Find the area of quadrilateral ABCD whose vertices are A(-5, 7), B(-4, -5) C(-1,-6) and D(4,5)
If the point P(k - 1, 2) is equidistant from the points A(3, k) and B(k, 5), find the value of k.
If `P(a/2,4)`is the mid-point of the line-segment joining the points A (−6, 5) and B(−2, 3), then the value of a is
The abscissa of any point on y-axis is
The area of the triangle formed by the points A(2,0) B(6,0) and C(4,6) is
Find the centroid of the triangle whose vertices is (−2, 3) (2, −1) (4, 0) .
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.
If the distance between points (x, 0) and (0, 3) is 5, what are the values of x?
Write the coordinates of a point on X-axis which is equidistant from the points (−3, 4) and (2, 5).
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.
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?
The coordinates of the point on X-axis which are equidistant from the points (−3, 4) and (2, 5) are
The distance of the point (4, 7) from the x-axis is
The point on the x-axis which is equidistant from points (−1, 0) and (5, 0) is
If A(x, 2), B(−3, −4) and C(7, −5) are collinear, then the value of x is
