Advertisements
Advertisements
Question
If the coordinates of the middle point of the portion of a line intercepted between the coordinate axes is (3, 2), then the equation of the line will be ______.
Options
2x + 3y = 12
3x + 2y = 12
4x – 3y = 6
5x – 2y = 10
Solution
If the coordinates of the middle point of the portion of a line intercepted between the coordinate axes is (3, 2), then the equation of the line will be 2x + 3y = 12.
Explanation:
Let the given line meets the axes at A(a, 0) and B(0, b).
Given that C(3, 2) is the mid-point of AB
∴ 3 = (a + 0)/2`
⇒ a = 6
And 2 =
⇒ b = 4
Intercept form of the line AB
⇒
⇒ 2x + 3y = 12
APPEARS IN
RELATED QUESTIONS
Prove that the line through the point (x1, y1) and parallel to the line Ax + By + C = 0 is A (x –x1) + B (y – y1) = 0.
Find the equation of the line passing through the point of intersection of the lines 4x + 7y – 3 = 0 and 2x – 3y + 1 = 0 that has equal intercepts on the axes.
Find equation of the line which is equidistant from parallel lines 9x + 6y – 7 = 0 and 3x + 2y + 6 = 0.
Prove that the product of the lengths of the perpendiculars drawn from the points
Find the equation of a line making an angle of 150° with the x-axis and cutting off an intercept 2 from y-axis.
Find the lines through the point (0, 2) making angles
Find the equations of the sides of the triangles the coordinates of whose angular point is respectively (1, 4), (2, −3) and (−1, −2).
Point R (h, k) divides a line segment between the axes in the ratio 1 : 2. Find the equation of the line.
Find the equation of a line for p = 8, α = 300°.
Put the equation
Find the values of θ and p, if the equation x cos θ + y sin θ = p is the normal form of the line
Reduce the equation 3x − 2y + 6 = 0 to the intercept form and find the x and y intercepts.
Find the area of the triangle formed by the line x + y − 6 = 0, x − 3y − 2 = 0 and 5x − 3y + 2 = 0.
Find the coordinates of the incentre and centroid of the triangle whose sides have the equations 3x− 4y = 0, 12y + 5x = 0 and y − 15 = 0.
Prove that the following sets of three lines are concurrent:
Find the conditions that the straight lines y = m1 x + c1, y = m2 x + c2 and y = m3 x + c3 may meet in a point.
Find the image of the point (2, 1) with respect to the line mirror x + y − 5 = 0.
If a ≠ b ≠ c, write the condition for which the equations (b − c) x + (c − a) y + (a − b) = 0 and (b3 − c3) x + (c3 − a3) y + (a3 − b3) = 0 represent the same line.
If the lines x + q = 0, y − 2 = 0 and 3x + 2y + 5 = 0 are concurrent, then the value of q will be
Find the equation of the line where length of the perpendicular segment from the origin to the line is 4 and the inclination of the perpendicular segment with the positive direction of x-axis is 30°.
Find the equation of the straight line which passes through the point (1, – 2) and cuts off equal intercepts from axes.
Find the equation of the lines which passes through the point (3, 4) and cuts off intercepts from the coordinate axes such that their sum is 14.
If the intercept of a line between the coordinate axes is divided by the point (–5, 4) in the ratio 1 : 2, then find the equation of the line.
If the line
Reduce the following equation into slope-intercept form and find their slopes and the y-intercepts.
x + 7y = 0
Reduce the following equation into intercept form and find their intercepts on the axes.
4x – 3y = 6
