Line passes through the point and makes an inclination of with the positive -axis

MATHEMATICS · Multi-part · A Level · Mathematics · Coordinate geometry in the (x y) plane · Coordinate geometry in the (x y) plane

Problem

Line

L

passes through the point

A(1,2)

and makes an inclination of

60^{\circ}

with the positive

x

-axis. Another line

M

passes through the point

B(3,-1)

and is perpendicular to

L

. (i) Find the equation of line

L

. (ii) Obtain the equation of line

M

. (iii) Locate the coordinates of their intersection point

C

. (iv) Calculate the angle between lines

L

and

M

and comment on your result.