Question 1: Calculate the distance between the points correct to decimal places.

Answer:

Question 2: Find the distance between the points correct to significant figures.

Answer:

Question 3: Show that the points form an equilateral triangle.

Answer:

Therefore three sides are equal which makes it an equilateral triangle.

Question 4: The circle with center passes though the points . Find the values of

Answer:

Distance of the points from the center are equal. Therefore

… … … … i)

… … … … ii)

Solving i) and ii), we get .

Therefore the center is

Question 5: The points are such that . Find a linear relation between

Answer:

Question 6: Given a triangle in which . A point lies on such that . Find the length of line segment

Answer:

A point lies on such that .

Therefore

Length of

Question 7: are two fixed points. Find the co-ordinates of the point in such that: . Also, find the co-ordinates of some other point such that

Answer:

For P When Ratio:

Therefore

For Q When Ratio:

Therefore

Question 8: are the vertices of a triangle . Point lies on lies on such that . Show that:

Answer:

When Ratio:

Therefore

When Ratio:

Therefore

Question 9: Find the coordinates of points of trisection of the line segment joining the point and the origin.

Answer:

Let be the two points dividing the points and the origin in the ratio 1:2 \text{ and } 2:1 respectively.

Therefore

Therefore

Question 10: 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:

Therefore

Question 11: 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 12: The mid-point of the segment , as shown in diagram, is . Write down the coordinates of [1996]

Answer:

Therefore

Question 13: is a diameter of a circle with center . If , find

(i) the length of radius

(ii) the coordinates of [2013]

Answer:

Therefore

Question 14: Find the co-ordinates of the centroid of a triangle whose vertices are : [2006]

Answer:

Let be the centroid of triangle .

Therefore

Hence the coordinates of the centroid are

Question 15: The mid-point of the line segment joining . Find the values of

Answer:

Therefore

Question 16: The mid-point of the line segment joining . Find the values of . [2007]

Answer:

Therefore

Question 17: (i) Write down the co-ordinates of the point that divides the line joining in the ratio .

(ii) Calculate the , where is the origin.

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

Answer:

i) For P When Ratio:

Therefore

ii)

iii) Let the required ratio be and the point be

Question 18: 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 19: is the mid-point of the line segment joining the points . Find the coordinates of point . Further, if divides the line segment joining and the origin in the ratio , find the ratio

Answer:

For M When Ratio:

Therefore

Let divide MO in the ratio

Question 20: 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