Question 1: Which of the following points lie on the line :

Answer:

which is true.

and therefore lies on the equation.

which is NOT true.

does not satisfies the equation and therefore does not lies on the equation.

which is true.

and therefore lies on the equation.

which is true.

and therefore lies on the equation.

which is NOT true.

does not satisfies the equation and therefore does not lies on the equation.

which is NOT true.

does not satisfies the equation and therefore does not lies on the equation.

Question 2: State, true or false:

,

Answer:

which is NOT true.

and therefore the equation does not pass through the given point.

which is true.

and therefore the equation does not pass through the given point.

which is true.

and therefore the equation passes through the given point.

which is true.

and therefore the equation passes through the given point.

if and not when .

Question 3: The line given by the equation passes through the point ; calculate the value of

Answer:

then k = 4.5

Question 4: For what value of will the point lie on the line

Answer:

Question 5: The line contains the point ; calculate the value of

Answer:

Question 6: Does the line bisect the join of ?

Answer:

Ratio for being a midpoint:

Let the coordinates of the point

Therefore

which is true.

satisfies the equation .

Hence the mid point is on the given line and bisects the given points.

Question 7:

i) The line bisects the join of , find the value of

ii) The line bisects the join of . Find the value of

Answer:

i) Ratio for being a midpoint:

Let the coordinates of the point

Therefore

ii) Ratio for being a midpoint:

Let the coordinates of the point

Therefore

Question 8:

i) The point lies on the line , calculate the value of

ii) The line contains the point , calculate the value of

Answer:

Question 9: The point divides the join of in the ratio of . Does lie on the line ?

Answer:

Let the coordinates of the point

Therefore

which is true.

and therefore lies on the equation.

Question 10: The line segment joining the points is divided by the point . Does the line contain ?

Answer:

Let the coordinates of the point

Therefore

which is true.

and therefore lies on the equation.

Question 11: Find the point of intersection of the lines . If this point lies on the line , find the value of

Answer:

Solving the two equations:

Substituting

Hence the point of intersection

Question 12: Show that the lines , are concurrent.

Answer:

Solving the two equations first:

Hence the point of intersection of the two lines is

If satisfies , then the three lines are concurrent.

Hence the lines are concurrent.