Page 43 - 12 Math 4

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EXERCISE 4.3

1. Find the slope and inclination o f the line joining the points:
(i) (-2, 4) ; (5, 11) (ii) (3, -2) ; (2, 7) (iii) (4, 6) ; (4, 8)
Sketch each line in the plane.

2. In the triangle A (8, 6) B (-4, 2), C (-2 , -6) , find the slope of
(i) each side of the triangle
(ii) each median of the triangle
(iii) each altitude of the triangle.

3. By means of slopes, show that the following points lie on the same line:
(a) (-1, -3) ; (1, 5) ; (2, 9) (b) (4 ,-5) ; (7, 5) ; (10, 15)
(c) (-4, 6) ; (3, 8) ; (10, 10) (d) (a, 2b): (c, a + b); (2c - a, 2a)

4. Find k so that the line joining A (7, 3); B (k, -6) and the line joining C (-4, 5) ; D (-6, 4)
are (i) parallel (ii) perpendicular.

5. Using slopes, show that the triangle with its vertices A (6, 1), B (2, 7) and C (-6, -7) is a
right triangle.

6. The three points A (7, -1), B (-2, 2) and C (1, 4) are consecutive vertices of a
parallelogram. Find the fourth vertex.

7. The points A (-1, 2), B (3, -1) and C (6, 3) are consecutive vertices
of a rhombus. Find the fourth vertex and show that the diagonals of the rhombus
are perpendicular to each other.
8. Two pairs of points are given. Find whether the two lines determined by these points
are :
(i) parallel (ii) perpendicular (iii) none.
(a) (1, -2), (2, 4) and (4, 1), (-8, 2)
(b) (-3, 4 ), (6, 2) and (4, 5), (-2, -7)
9. Find an equation of
(a) the horizontal line through (7, -9)
(b) the vertical line through (-5, 3)

version: 1.1

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