# NCERT Mathematics Class 10 Exemplar Ch 7 Coordinate Geometry Part 4

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**EXERCISE 7.3**

1. Name the type of triangle formed by the points , and .

Answer: Scalene triangle

2. Find the points on the x–axis which are at a distance of from the point How many such points are there?

Answer: points

3. What type of a quadrilateral do the points , and taken in that order, form?

Answer: Rectangle

4. Find the value of a , if the distance between the points and is 9 units.

Answer:

5. Find a point which is equidistant from the points and ? How many such points are there?

Answer: the middle point of AB. Infinite number of points. In fact, all points which are solutions of the equation .

6. Find the coordinates of the point Q on the x–axis which lies on the perpendicular bisector of the line segment joining the points and . Name the type of triangle formed by the points Q, A and B.

Answer: isosceles triangle

7. Find the value of m if the points , and are collinear.

Answer:

8. If the point is equidistant from and , find the values of y. Also find distance PQ.

Answer:

9. Find the area of the triangle whose vertices are and .

Answer: 0

10. In what ratio does the x–axis divide the line segment joining the points and ? Find the coordinates of the point of division.

Answer: , ,

11. Find the ratio in which the point P divides the line segment joining the points , and .

Answer:

12. If divides line segment joining and in the ratio , find the values of a and b.

Answer:

13. If (a, b) is the mid-point of the line segment joining the points and and , find the value of k and the distance AB.

Answer: ,

14. The centre of a circle is . Find the values of an if the circle passes through the point and has diameter units.

Answer: