Advertisements
Advertisements
Question
The equation of the line joining the point (3, 5) to the point of intersection of the lines 4x + y – 1 = 0 and 7x – 3y – 35 = 0 is equidistant from the points (0, 0) and (8, 34).
Options
True
False
Solution
This statement is True.
Explanation:
Given equations are
4x + y – 1 = 0 ......(i)
And 7x – 3y – 35 = 0 ......(ii)
From equation (i) y = 1 – 4x ......(iii)
Putting the value of y in equation (ii) we get
7x – 3(1 – 4x) – 35 = 0
⇒ 7x – 3 + 12x – 35 = 0
⇒ 19x – 38 = 0
⇒ x = 2
From equation (iii) we get,
y = 1 – 4 × 2
⇒ y = – 7
The point of intersection is (2, – 7).
Equation of line joining the point (3, 5) to the point (2, – 7) is
y – 5 = `(-7 - 5)/(2 - 3) (x - 3)`
⇒ y – 5 = 12(x – 3)
⇒ y – 5 = 12x – 36
⇒ 12x – y – 31 = 0 .......(iv)
Distance of equation (iv) from the point (0, 0)
= `|(-31)/sqrt((12)^2 + (-1)^2)|`
= `31/sqrt(145)`
Distance of equation (iv) from the point (8, 34) is
= `|(12 xx 8 - 34 - 31)/sqrt((12)^2 + (-1)^2)|`
= `|(96 - 65)/sqrt(145)|`
= `31/sqrt(145)`
APPEARS IN
RELATED QUESTIONS
Find the equations of the straight lines which pass through (4, 3) and are respectively parallel and perpendicular to the x-axis.
Find the equation of the straight line passing through the point (6, 2) and having slope − 3.
Find the equation of the straight line passing through (−2, 3) and inclined at an angle of 45° with the x-axis.
Find the equation of the line passing through (0, 0) with slope m.
Find the equation of the line passing through \[(2, 2\sqrt{3})\] and inclined with x-axis at an angle of 75°.
Prove that the perpendicular drawn from the point (4, 1) on the join of (2, −1) and (6, 5) divides it in the ratio 5 : 8.
Find the equation of the straight lines passing through the following pair of point :
(0, −a) and (b, 0)
Find the equation of the straight lines passing through the following pair of point :
(a cos α, a sin α) and (a cos β, a sin β)
Find the equations of the sides of the triangles the coordinates of whose angular point is respectively (0, 1), (2, 0) and (−1, −2).
Find the equations to the diagonals of the rectangle the equations of whose sides are x = a, x = a', y= b and y = b'.
In what ratio is the line joining the points (2, 3) and (4, −5) divided by the line passing through the points (6, 8) and (−3, −2).
The vertices of a quadrilateral are A (−2, 6), B (1, 2), C (10, 4) and D (7, 8). Find the equation of its diagonals.
Find the equation of a line which passes through the point (22, −6) and is such that the intercept of x-axis exceeds the intercept of y-axis by 5.
Find the equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.
Find the equation of the straight line which passes through the point P (2, 6) and cuts the coordinate axes at the point A and B respectively so that \[\frac{AP}{BP} = \frac{2}{3}\] .
Find the equations of the straight lines which pass through the origin and trisect the portion of the straight line 2x + 3y = 6 which is intercepted between the axes.
The straight line through P (x1, y1) inclined at an angle θ with the x-axis meets the line ax + by + c = 0 in Q. Find the length of PQ.
Find the equation of the straight line passing through the point of intersection of the lines 5x − 6y − 1 = 0 and 3x + 2y + 5 = 0 and perpendicular to the line 3x − 5y + 11 = 0 .
Find the equation of a line passing through the point (2, 3) and parallel to the line 3x − 4y + 5 = 0.
The line 2x + 3y = 12 meets the x-axis at A and y-axis at B. The line through (5, 5) perpendicular to AB meets the x-axis and the line AB at C and E respectively. If O is the origin of coordinates, find the area of figure OCEB.
Find the length of the perpendicular from the point (4, −7) to the line joining the origin and the point of intersection of the lines 2x − 3y + 14 = 0 and 5x + 4y − 7 = 0.
Find the equations to the straight lines passing through the point (2, 3) and inclined at and angle of 45° to the line 3x + y − 5 = 0.
If a, b, c are in G.P. write the area of the triangle formed by the line ax + by + c = 0 with the coordinates axes.
The equation of the line passing through (1, 5) and perpendicular to the line 3x − 5y + 7 = 0 is
Find the equation of lines passing through (1, 2) and making angle 30° with y-axis.
Find the equations of the lines through the point of intersection of the lines x – y + 1 = 0 and 2x – 3y + 5 = 0 and whose distance from the point (3, 2) is `7/5`
The equation of the line passing through the point (1, 2) and perpendicular to the line x + y + 1 = 0 is ______.
If a, b, c are in A.P., then the straight lines ax + by + c = 0 will always pass through ______.
