Consider two non-vertical straight lines and with slopes and respectively.

MATHEMATICS · Multi-part · CBSE · Mathematics · Straight Lines · Straight Lines

Problem

Consider two non-vertical straight lines

L_1

and

L_2

with slopes

m_1

and

m_2

respectively. (i) State the algebraic condition that

m_1

and

m_2

must satisfy for

L_1

and

L_2

to be perpendicular. (ii) Give a brief geometrical explanation, using the concept of the angle a line makes with the

x

-axis, to show why the condition obtained in part (i) ensures that the angle between

L_1

and

L_2

90^{\circ}

. (iii) The line

L_1

is given by

y = 3x + 1

. Without forming any new equation, examine whether the line

2y + \dfrac{1}{3}x - 7 = 0

is perpendicular to

L_1

. Justify your answer using the condition stated in part (i).