Locus and Straight Line(p-1) Maths (commerce) - Locus and Straight Line(p-1)

Obtain the equation of the line containing the point: (2, 5) and perpendicular to the X-axis.

Obtain the equation of the line containing the point: (2, 4) and perpendicular to the Y-axis.

Obtain the equation of the line containing the point: (2, 3) and parallel to the X-axis.

Obtain the equation of the line which is: parallel to the Y-axis and making an intercept of 3 on the X-axis.

Obtain the equation of the line which is: parallel to the X-axis and making an intercept of 5 on the Y-axis.

Find the equation of the line passing through the points A(-3, 0) and B(0, 4).

Does point A(2, 3) lie on the line 3x + 2y – 6 = 0? Give reason.

D(-1, 8), E(4, -2), F(-5, -3) are midpoints of sides BC, CA and AB of ∆ABC. Find
(i) equations of sides of ∆ABC.
(ii) co-ordinates of the circumcentre of ∆ABC.

Find the slope, x-intercept, y-intercept of each of the following lines.
(a) 2x + 3y – 6 = 0
(b) x + 2y = 0

The vertices of a triangle are A(3, 4), B(2, 0), and C(-1, 6). Find the equations of
(a) side BC
(b) the median AD
(c) the midpoints of sides AB and BC.

Write the equation of the line:
(a) parallel to the X-axis and at a distance of 5 units from it and above it.
(b) parallel to the Y-axis and at a distance of 5 units from it and to the left of it.
(c) parallel to the X-axis and at a distance of 4 units from the point (-2, 3).

If the line 3x + 4y = p makes a triangle of area 24 square units with the co-ordinate axes, then find the value of p.

Line y = mx + c passes through the points A(2, 1) and B(3, 2). Determine m and c.

If the origin is shifted to the point O'(1, 3), the axes remaining parallel to the original axes, find the old co-ordinates of the points (a) C(5, 4) (b) D(3, 3)

If the origin is shifted to the point O'(2, 3), the axes remaining parallel to the original axes, find the new co-ordinates of the points (a) A(1, 3) (b) B(2, 5)

Find the equation of the line passing through the point of intersection of lines x + y – 2 = 0 and 2x – 3y + 4 = 0 and making intercept 3 on the X-axis.

Find the co-ordinates of the circumcentre of the triangle whose vertices are A(-2, 3), B(6, -1), C(4, 3).

Find the equations of the altitudes of the triangle whose vertices are A(2, 5), B(6, -1) and C(-4, -3).