Advertisements
Advertisements
Question
In the adjoining figure, write
(i) The coordinates of A, B and C.
(ii) The equation of the line through A and | | to BC.
Solution
(i) A = (2, 3), B = (-1, 2), C = (3, 0).
(ii) Slope of BC = `(y_2 - y_1)/(x_2 - x_1) = (2 - 0)/(-1 - 3) = (2)/(-4)`
m1 = `(-1)/(2)`
Since lines are parallel
∴ m1 = m2
Hence, m2 = `-(1)/(2)`
and passing through point (2, 3)
∵ Equation of line is y - y1 = m2 (x - x1)
∴ required line is y - 3 = `(-1)/(2)(x - 2)`
2y - 6 = -x + 2
x + 2y = 8.
APPEARS IN
RELATED QUESTIONS
A(-1, 3), B(4, 2) and C(3, -2) are the vertices of a triangle.
1) Find the coordinates of the centroid G of the triangle
2) Find the equation of the line through G and parallel to AC
State, true or false :
The line `x/2 + y/3 = 0` passes through the point (4, −6).
The line segment joining the points (5, −4) and (2, 2) is divided by the points Q in the ratio 1 : 2. Does the line x – 2y = 0 contain Q?
Find the equation of a line which passes through (5, 4) and makes an angle of 60° with the positive direction of the x-axis.
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 if the following points lie on the given line or not:
(7, -2) on the line 5x + 7y = 11
Find the equation of a line passing through (2,5) and making and angle of 30° with the positive direction of the x-axis.
Find the equation of a line passing through (2,9) and parallel to the line 3x + 4y = 11
Find the equation of a line passing through the intersection of x + 2y + 1= 0 and 2x - 3y = 12 and perpendicular to the line 2x + 3y = 9
The coordinates of two points P and Q are (0,4) and (3,7) respectively. Find
(i) The gradient of PQ
(ii) the equation of PQ
(iii) the coordinates of the point where the line AB intersects the X-axis.
