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: