Find the ratio in which the line segment joining the points (2, 3) and (4, 5) is divided by the line joining (6, 8) and (–3, –2).
5 : 7
The equation of the line passing through (6, 8) and (–3, –2) is
⇒ 9y – 72 = 10x – 60
or 10x – 9y + 12 = 0 … (i)
Let the required ratio be λ : 1.
Now the coordinates of the point P which divides the line segment joining the points (2, 3) and (4, 5) in the ratio λ : 1 is
Clearly P lies on (i), then
∴ The required ratio,
= –5 : 7
Hence the required ratio is 5 : 7 (externally).
Find the equation to the straight line cutting off an intercept of 5 units on negative direction of y-axis and being equally inclined to the axes.
Find the equations of the bisectors of the angle between the coordinate axes.
Find the equation of a line which makes an angle of 135o with positive direction of x-axis and passes through the point (3, 5).
Find the equation of the straight line bisecting the segment joining the points (5, 3) and (4, 4) and making an angle of 45o with the positive direction of x-axis.
Find the equation of the right bisector of the line joining (1, 1) and (3, 5).
Find the equation to the straight line joining the points .
Let ABC be a triangle with A(–1, –5), B(0, 0) and C(2, 2) and let D be the middle point of BC. Find the equation of the perpendicular drawn from Bto AD.
The vertices of a triangle are A(10, 4), B(–4, 9) and C(–2, –1). Find the equation of the altitude through A.
Find the equations of the medians of a triangle, the coordinates of whose vertices are (–1, 6), (–3, –9) and (5, –8).
Find the equation of the line through (2, 3) so that the segment of the line intercepted between the axes is bisected at this point.