Advertisements
Advertisements
Question
In the following diagram, write down:
- the co-ordinates of the points A, B and C.
- the equation of the line through A and parallel to BC.
Solution
i. The co-ordinates of points A, B and C are (2, 3), (−1, 2) and (3, 0) respectively.
ii. Slope of BC = `(0 - 2)/(3 +1) = (-2)/4 = (-1)/2`
Slope of a line parallel to BC = Slope of BC = `(-1 )/2`
Required equation of a line passing through A and parallel to BC is given by
y − y1 = m(x − x1)
`y − 3 = (-1)/2 (x − 2)`
2y − 6 = −x + 2
x + 2y = 8
APPEARS IN
RELATED QUESTIONS
Find the equation of the line passing through (5, –3) and parallel to x – 3y = 4.
A(1, −5), B(2, 2) and C(−2, 4) are the vertices of triangle ABC. Find the equation of the altitude of the triangle through B.
A(1, −5), B(2, 2) and C(−2, 4) are the vertices of triangle ABC. Find the equation of the line through C and parallel to AB.
Point P divides the line segment joining the points A(8, 0) and B(16, –8) in the ratio 3 : 5. Find its co-ordinates of point P. Also, find the equation of the line through P and parallel to 3x + 5y = 7.
Given a straight line x cos 30° + y sin 30° = 2. Determine the equation of the other line which is parallel to it and passes through (4, 3).
Find the value of k such that the line (k – 2)x + (k + 3)y – 5 = 0 is:
- perpendicular to the line 2x – y + 7 = 0
- parallel to it.
Find the slope of a line perpendicular to the foloowing line 4x + y = 7
Find the value of a line perpendicular to the given line 2x-3y = 4
Find the relation connecting p and q, if the lines py = 2x + 5 and qx + 3y = 2 are parallel to each other.
Find the relation connecting a and b, if the lines ay = 2x + 4 and 4y + bx = 2 are perpendicular to each other.
