10th Samacheer Kalvi Math Solution for Exercise 5.3

This page 10th Samacheer Kalvi Math Solution for Exercise 5.3 is going to provide you solution for every problems that you find in the exercise no 5.3

10th Samacheer Kalvi Math Solution for Exercise 5.3

1. Find the angle of inclination of the straight line whose slope is (i) 1 (ii) √3 (iii) 0

2. Find the slope of the straight line whose angle of inclination is (i) 30° (ii) 60° (iii) 90°

3. Find the slope of the straight line passing through the points

(i) (3 , -2) and (7 , 2)

(ii) (2 , -4) and origin

(iii) (1 + √3 , 2) and (3 + √3 , 4)

4. Find the angle of inclination of the line passing through the points (i) (1, 2) and (2 , 3)

(ii) (3 , 3) and (0 , 0)

(iii) (a , b) and (-a , -b)

5. Find the slope of the line which passes through the origin and the midpoint ofthe line segment joining the points (0 ,- 4) and (8 , 0).

6. The side AB of a square ABCD is parallel to x-axis . Find the (i) slope of AB (ii) slope of BC (iii) slope of the diagonal AC

7. The side BC of an equilateralΔ ABC is parallel to x-axis. Find the slope of AB and the slope of BC

8. Using the concept of slope, show that each of the following set of points are collinear.

(i) (2 , 3), (3 , -1) and (4 , -5)

(ii) (4 , 1), (-2 , -3) and (-5 , -5)

(iii) (4 , 4), (-2 , 6) and (1 , 5)

9. If the points (a, 1), (1, 2) and (0, b+1) are collinear, then show that (1/a) + (1/b) = 1

10. The line joining the points A(-2 , 3) and B(a , 5) is parallel to the line joining the points C(0 , 5) and D(-2 , 1). Find the value of a.

11. The line joining the points A(0, 5) and B(4, 2) is perpendicular to the line joining the points C(-1, -2) and D(5, b). Find the value of b.

12. The vertices of 3ABC are A(1, 8), B(-2, 4), C(8, -5). If M and N are the midpoints of AB and AC respectively, find the slope of MN and hence verify that MN is parallel to BC.

13. A triangle has vertices at (6 , 7), (2 , -9) and (-4 , 1). Find the slopes of its medians.

14. The vertices of a 3ABC are A(-5 , 7), B(-4 , -5) and C(4,5). Find the slopes of the altitudes of the triangle.

15. Using the concept of slope, show that the vertices (1 , 2), (-2 , 2), (-4 , -3) and (-1, -3) taken in order form a parallelogram.

16. Show that the opposite sides of a quadrilateral with vertices A(-2 ,-4), B(5 , -1), C(6 , 4) and D(-1, 1) taken in order are parallel. 10th samacheer kalvi math solution for exercise 5.3