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
Advertisements
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 equation of the line parallel to x-axis and having intercept − 2 on y-axis.
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 \[(2, 2\sqrt{3})\] and inclined with x-axis at an angle of 75°.
Find the equation of the straight line passing through (3, −2) and making an angle of 60° with the positive direction of y-axis.
Find the equation of the straight line which divides the join of the points (2, 3) and (−5, 8) in the ratio 3 : 4 and is also perpendicular to it.
Find the equation of the straight lines passing through the following pair of point:
(a, b) and (a + c sin α, b + c cos α)
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 :
(at1, a/t1) and (at2, a/t2)
Find the equations of the medians of a triangle, the coordinates of whose vertices are (−1, 6), (−3, −9) and (5, −8).
By using the concept of equation of a line, prove that the three points (−2, −2), (8, 2) and (3, 0) are collinear.
Find the equation to the straight line which bisects the distance between the points (a, b), (a', b') and also bisects the distance between the points (−a, b) and (a', −b').
The owner of a milk store finds that he can sell 980 litres milk each week at Rs 14 per liter and 1220 liters of milk each week at Rs 16 per liter. Assuming a linear relationship between selling price and demand, how many liters could he sell weekly at Rs 17 per liter.
Find the equation to the straight line cutting off intercepts 3 and 2 from the axes.
Find the equation to the straight line which cuts off equal positive intercepts on the axes and their product is 25.
Find the equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.
A straight line drawn through the point A (2, 1) making an angle π/4 with positive x-axis intersects another line x + 2y + 1 = 0 in the point B. Find length AB.
Find the equation of straight line passing through (−2, −7) and having an intercept of length 3 between the straight lines 4x + 3y = 12 and 4x + 3y = 3.
Find the equation of the straight line through the point (α, β) and perpendicular to the line lx + my + n = 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 equation of the straight lines passing through the origin and making an angle of 45° with the straight line \[\sqrt{3}x + y = 11\].
Find the equations to the straight lines which pass through the point (h, k) and are inclined at angle tan−1 m to the straight line y = mx + c.
Find the equations to the sides of an isosceles right angled triangle the equation of whose hypotenues is 3x + 4y = 4 and the opposite vertex is the point (2, 2).
Find the equations of two straight lines passing through (1, 2) and making an angle of 60° with the line x + y = 0. Find also the area of the triangle formed by the three lines.
The equation of the base of an equilateral triangle is x + y = 2 and its vertex is (2, −1). Find the length and equations of its sides.
Find the equation of the straight line which passes through the point of intersection of the lines 3x − y = 5 and x + 3y = 1 and makes equal and positive intercepts on the axes.
Find the equations of the lines through the point of intersection of the lines x − 3y + 1 = 0 and 2x + 5y − 9 = 0 and whose distance from the origin is \[\sqrt{5}\].
Write the integral values of m for which the x-coordinate of the point of intersection of the lines y = mx + 1 and 3x + 4y = 9 is an integer.
Find the locus of the mid-points of the portion of the line x sinθ+ y cosθ = p intercepted between the axes.
A straight line moves so that the sum of the reciprocals of its intercepts made on axes is constant. Show that the line passes through a fixed point.
The equations of the lines which pass through the point (3, –2) and are inclined at 60° to the line `sqrt(3) x + y` = 1 is ______.
The straight line 5x + 4y = 0 passes through the point of intersection of the straight lines x + 2y – 10 = 0 and 2x + y + 5 = 0.
The lines ax + 2y + 1 = 0, bx + 3y + 1 = 0 and cx + 4y + 1 = 0 are concurrent if a, b, c are in G.P.
