Advertisements
Advertisements
प्रश्न
The figure given alongside shows two straight lines AB and CD intersecting each other at point P(3, 4). Find the equations of AB and CD.
उत्तर
Slope of line AB = tan 45° = 1
The line AB passes through P(3, 4).
So, the equation of the line AB is given by:
y − y1 = m(x − x1)
y − 4 = 1(x − 3)
y − 4 = x − 3
y = x + 1
Slope of line CD = tan 60° = `sqrt(3)`
The line CD passes through P(3, 4).
So, the equation of the line CD is given by:
y − y1 = m(x − x1)
`y - 4 = sqrt(3)(x − 3)`
`y - 4 = sqrt(3)x − 3sqrt(3)`
`y = sqrt(3)x + 4 − 3sqrt(3)`
APPEARS IN
संबंधित प्रश्न
Solve the following inequation and represent the solution set on a number line.
`-8 1/2 < -1/2 -4x <= 7 1/2`, x ∈ 1
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 :
The point (8, 7) lies on the line y – 7 = 0
Find the equation of the line passing through : (−1, −4) and (3, 0)
Find the equation of the straight line passing through origin and the point of intersection of the lines x + 2y = 7 and x – y = 4.
In triangle ABC, the co-ordinates of vertices A, B and C are (4, 7), (–2, 3) and (0, 1) respectively. Find the equation of median through vertex A. Also, find the equation of the line through vertex B and parallel to AC.
Write down the equation of the line whose gradient is `-2/5` and which passes through point P, where P divides the line segement joining A(4, −8) and B(12, 0) in the ratio 3 : 1.
A line 5x + 3y + 15 = 0 meets y-axis at point P. Find the co-ordinates of points P. Find the equation of a line through P and perpendicular to x – 3y + 4 = 0.
Determine whether the line through points (–2, 3) and (4, 1) is perpendicular to the line 3x = y + 1.
Does line 3x = y + 1 bisect the line segment joining the two given points?
Find the value of ‘a’ for which the following points A (a, 3), B (2, 1) and C (5, a) are collinear. Hence find the equation of the line.
