Advertisements
Advertisements
Question
The line 7x - 8y = 4 divides join of (-8,-4) and (6,k) in the ratio of 2 : 5. Find the value of k.
Solution
Let the point of intersection of AB and the line 7x-8y=4, be the point P (a,b)
Also, given the line 7x-8y = 4 divides the line segment AB in the ratio 2 : 5.
i.e. AP: PB = 2: 5
Coordinates of P are,
P (a,b) = P `((12 - 40)/7 , (2"k" - 20)/7) = "P" (-4, (2"k" - 20)/7)`
P (a,b) lies on the line 7x - 8y = 4,
P will satisfy the equation of the line
7(-4) - `((2"k" - 20)/7)` = 4
-8 `((2"k" - 20)/7)` = 32
2k - 20 = -28
2k = -8
k = -4
APPEARS IN
RELATED QUESTIONS
State, true or false :
If the point (2, a) lies on the line 2x – y = 3, then a = 5.
Find the equation of the line passing through : (−1, −4) and (3, 0)
A straight line passes through the point (3, 2) and the portion of this line, intercepted between the positive axes, is bisected at this point. Find the equation of the line.
Write down the equation of the line whose gradient is `3/2` and which passes through P, where P divides the line segment joining A(−2, 6) and B(3, −4) in the ratio 2 : 3.
The vertices of a ΔABC are A(3, 8), B(–1, 2) and C(6, –6). Find:
(i) Slope of BC
(ii) Equation of a line perpendicular to BC and passing through A.
Find if the following points lie on the given line or not:
(2,4) on the line y = 2x - 1
Find if the following points lie on the given line or not:
(-1, 5) on the line 3x = 2y -15
Find the value of m if the line 2x + 5y + 12 = 0 passes through the point
( 4,m ).
Find the equation of a line whose slope and y-intercept are m = `(-6)/5`, c = 3
Find the equation of a line passing through (8,3) and making an angle of 45° with the positive direction of the y-axis.
