Question 1: A line segment joining is divided in the ratio , the point where the line segment intersects the

(i) Calculate the value of

(ii) Calculate the co-ordinates of [1994]

Answer:

Question 2: In what ratio is the line joining divided by the ? Write the co-ordinates of the point where intersects the [1993]

Answer:

Let the required ratio be and the point of be

Question 3: The mid-point of the segment , as shown in diagram, is Write down the coordinates of [1996]

Answer:

Therefore

Question 4: is a diameter of a circle with center If , find

(i) the length of radius

(ii) the coordinates of [2013]

Answer:

Therefore

Question 5: Find the co-ordinates of the centroid of a triangle whose vertices are : [2006]

Answer:

Let be the centroid of triangle

Therefore

Question 6: The mid-point of the line segment joining Find the values of [2007]

Answer:

Therefore

Question 7: (i) Write down the co-ordinates of the point that divides the line joining in the ratio

(ii) Calculate the distance , where is the origin.

(iii) In what ratio does the divide the line ? [1995]

Answer:

i) For P When Ratio:

Therefore

Therefore the point

ii)

iii) Let the required ratio be and the point be

Question 8: Prove that the points are the vertices of an isosceles right-angled triangle. Find the co-ordinates of so that is a square. [1992]

Answer:

(two sides are equal). Hence triangle is a isosceles triangle.

Question 9: Calculate the ratio in which the line joining is divided by point Also, find (i) (ii) length of [2014]

Answer:

Let divide MO in the ratio

Question 10: Calculate the ratio in which the line joining is divided by the line [2006]

Answer:

Let the required ratio be and the point of be

Now calculate the coordinate of the point of intersection

Co-ordinates of the point of intersection =

Question 11: lf

(i) find the length of

(ii) In what ratio is the line joining , divided by the ? [2008]

Answer:

Let the required ratio be and the point of be

Question 12: The line segment joining is intercepted by at the point Write down the ordinate of the point Hence, find the ratio in which divides Also, find the co-ordinates of the point [1990, 2006]

Answer:

Let the required ratio be and the point of be

Question 13: In the given figure, line meets the at point at point is the point Find the co-ordinates of [1999, 2013]

Answer:

Therefore

Question 14: Given a line segment joining the points Find:

i) The ratio in which is divided by

ii) Find the coordinates of point of intersection

iii) The length of [2012]

Answer:

Let the required ratio be and the point of intersection be

Length of

Question 15: is a straight line of units. If has the coordinates has the coordinates , find the value of [2004]

Answer:

are the two points.

Distance between them is units.

Therefore

Question 16: The mid point of the line segment joining (3m, 6) and (-4, 3n) is (1, 2m-1). Find the values of m and n. [2006]

Answer:

Therefore

Question 17: is a triangle and is the centroid of the triangle. If , find Find the length of the side [2011]

Answer:

is the centroid

units.