Mathematics
Given equation of line L1 is y = 4.
(i) Write the slope of line L2 if L2 is the bisector of angle O.
(ii) Write the co-ordinates of point P.
(iii) Find the equation of L2.
Answer
(i) The angle between x and y axis = 90°.
Given,
L2 is the bisector of angle O. So, inclination of line L2 is 45°.
Slope of L2 = tan 45° = 1.
Hence, slope of L2 = 1.
(ii) Equation of line L2, passing through origin (0, 0) and slope = 1 is :
⇒ y - y1 = m(x - x1)
⇒ y - 0 = 1(x - 0)
⇒ y = x.
From figure,
P is the point of intersection of y = 4 and y = x.
Solving,
y = 4 ……..(1)
y = x ……..(2)
Substituting value of y from (1) in (2) we get,
x = 4.
So, point of intersection = (4, 4).
Hence, P = (4, 4).
(iii) From part (ii) we get equation of L2 as,
y = x
Hence, equation of L2 is y = x.
Related Questions
A and B are the two points on the x-axis and y-axis respectively. P(2, -3) is the mid-point of AB.
Find :
(i) the coordinates of A and B.
(ii) the slope of the line AB.
(iii) the equation of the line AB.
ABCD is a parallelogram where A(x, y), B(5, 8), C(4, 7) and D(2, -4). Find
(i) the coordinates of A.
(ii) the equation of the diagonal BD.
Find the equation of the line that has x-intercept = -3 and is perpendicular to 3x + 5y = 1.
A straight line passes through the points P(-1, 4) and Q(5, -2). It intersects x-axis at point A and y-axis at point B. M is the mid-point of the line segment AB. Find :
(i) the equation of the line.
(ii) the co-ordinates of points A and B.
(iii) the co-ordinates of point M.