Reference Material for Preparation

Question 1: Find the equation of a line whose: ,

Answer:

Since , the corresponding point on

Given Slope

Therefore

Required equation of the line:

Question 2: Find the equation of a line whose:

Answer:

Since , the corresponding point on

Therefore

Required equation of the line:

Question 3: Find the equation of the line whose slope is and which passes through .

Answer:

Therefore

Required equation of the line:

Question 4: Find the equation of the line passing through and makes an angle of with the positive direction of .

Answer:

Therefore

Required equation of the line:

Question 5: Find the equation of the line passing through:

i)

ii)

Answer:

i)

Slope

Required equation of the line:

ii)

Slope

Required equation of the line:

Question 6: The co-ordinates of two points are respectively. Find:

i) The gradient of ;

ii) The equation of

iii) The co-ordinates of the point where intersects the .

Answer:

are respectively

Slope or PQ

Required equation of the line:

Question 7: The co-ordinates of two points are . Find:

i) The equation of ;

ii) The co-ordinates of the point where the line intersect the .

Answer:

are

Slope or AB

Required equation of the line:

Therefore when

Hence

Question 8: The figure given alongside shows two straight lines intersecting each other at point . Find the equations of .

Answer:

Slope of

Slope of

Equation of

Equation of

Question 9: In, . Find the equation of the median through .

Answer:

Let be the mid point of . Therefore the coordinates of are

Slope of

Equation of

Question 10: The following figure shows a parallelogram whose side is parallel to the , and vertex . Find the equations of .

Answer:

is parallel to

Slope of

Equation of

Slope of

Equation of

Question 11: Find the equation of the straight line passing through origin and the point of intersection of the lines and

Answer:

Solving and we get

Hence point of intersection

Slope of

Slope of

Question 12: In triangle , the co-ordinates of vertices are respectively. Find the equation of median through vertex . Also, find the equation of the line through vertex and parallel to .

Answer:

Let be the mid point of . Therefore the coordinates of are

Slope of

Equation of

Slope of

Equation of the line through vertex and parallel to

Question 13: have co-ordinates respectively. Find the equation of the line through and perpendicular to .

Answer:

Slope of

Slope of line perpendicular to

Therefore the equation of line perpendicular to BC and passing through A:

Question 14: Find he equation of the perpendicular dropped from the point onto the line joining the points .

Answer:

Slope of

Slope of line perpendicular to

Therefore the equation of line perpendicular to AB and passing through C:

Question 15: Find the equation of the line, whose:

i)

ii)

iii)

Answer:

i) Points given are

Slope

Equation of line:

ii) Points given are

Slope

Equation of line:

iii) Points given are

Slope

Equation of line:

Question 16: Find the equation of line whose slope is and .

Answer:

Slope , Intercept

Equation of the line:

Question 17: Find the equation of the line with and a point on it

Answer:

Given point are

Slope

Equation of the line:

Question 18: Find the equation of the line through and making an intercept of on the .

Answer:

Slope

Equation of the line:

Question 19: Find the equations of the lines passing through point and equally inclined to the co-ordinate axes.

Answer:

Given

Slope

Equation of line:

Also Slope

Equation of line:

Question 20: The line through intersects .

i) Write the slope of the line.

ii) Write the equation of the line.

iii) Find the co-ordinates of .

Answer:

Given points

Slope

Equation of line:

When

Hence the co-ordinates of

Question 21: Write down the equation of the line whose gradient is -and which passes through point , where divides the line segment joining in the ratio

Answer:

Ratio:

Let the coordinates of the point

Therefore

Therefore

Equation of line:

Question 22: are vertices of a triangle . Find:

i) The co-ordinates of the centroid of a triangle .

ii) The equation of a line through the centroid and parallel to .

Answer:

Let be the centroid. Therefore the coordinates of are:

Slope

Therefore the equation of a line parallel to will pass through

Equation of the line:

Question 23: are the vertices of a triangle . Find the equation of a line through the vertex and the point in ; such that .

Answer:

Ratio:

Let the coordinates of the point

Therefore

Therefore

Slope

Equation of the line: