Q9 of 319 Page 23

Show that the line joining (2, – 5) and (– 2, 5) is perpendicular to the line joining (6, 3) and (1,1).

To Prove: The Given line is perpendicular to each other.

Proof: Let Assume the coordinate A(2, – 5) and B(– 2, 5) joining the line AB, C(6,3) and D(1,1) joining the line CD.

The concept used: The product of the slopes of lines always – 1.

The formula used: The slope of the line, m =

Now, The slope of AB =

The Slope of AB =

Now, The slope of CD =

The Slope of AB =

So, AB × CD =

AB × CD = – 1

Hence, The given Lines are perpendicular to each other.

What can be said regarding a line if its slope is

(i) zero

(ii) positive

(iii) negative

Show that the line joining (2, – 3) and (– 5, 1) is parallel to the line joining (7, – 1) and (0, 3).

Without using Pythagoras theorem, show that the points A(0, 4), B(1, 2), C(3, 3) are the vertices of a right – angled triangle.

Prove that the points (– 4, – 1), (– 2, – 4), (4, 0) and (2, 3) are the vertices of a rectangle.