Advertisements
Advertisements
प्रश्न
The line 2x - 5y + 31 = 0 bisects the join of (-4,5) and (P, 9). Find the value of p.
उत्तर
Let the point of intersection of AB and the line 2x-5y+31 =O be the point R ( a,b)
Also, given the line 2x - 5y+31 =0 bisects the line segment AB
AR : RB = 1 : 1
Coordinates of R are,
R (a,b) = R `((-4 + "p")/2 , (5 + 9)/2) = R ((-4 + "p")/2 , 7)`
R (a,b) lies on the line 2x - 5y + 31 = 0
R will satisfy the equation of the line
2`((-4 + "p")/2)` - 5(7) + 31 = 0
⇒ (-4 + p) - 4 = 0
⇒ p = 8
APPEARS IN
संबंधित प्रश्न
The equation of a line 3x + 4y − 7 = 0. Find
1) The slope of the line.
2) The equation of a line perpendicular to the given line and passing through the intersection of the lines x – y + 2 = 0 and 3x + y – 10 = 0.
State, true or false :
If the point (2, a) lies on the line 2x – y = 3, then a = 5.
Find the equation of the perpendicular dropped from the point (−1, 2) onto the line joining the points (1, 4) and (2, 3).
Find the equations of the line through (1, 3) and making an intercept of 5 on the y-axis.
A(1, 4), B(3, 2) and C(7, 5) are vertices of a triangle ABC. Find the equation of a line, through the centroid and parallel to AB.
The line segment formed by the points (3, 7) and (-7, z) is bisected by the line 3x + 4y =18. Find the value of z.
P is a point on the line segment AB dividing it in the ratio 2 : 3. If the coordinates of A and Bare (-2,3) and (8,8), find if Plies on the line 7x - 2y =4.
Find the inclination of a line whose gradient is 0.4663
PQ is straight line of 13 units. If P has coordinate (2, 5) and Q has coordinate (x, – 7) find the possible values of x.
Find a general equation of a line which passes through:
(i) (0, -5) and (3, 0) (ii) (2, 3) and (-1, 2).
