and (

and ( b , to the line cos θ sin θ 1is b b . A person standing at the junction (crossing) of two straight paths represented by the equations x – y + = and x + y – = wants to reach the path whose equation is x – y + = in the least time. Find equation of the path that he should follow. Summary ® Slope ( m ) of a non-vertical line passing through the points ( x , y ) and ( x , y ) is given by m , ≠ ® If a line makes an angle á with the positive direction of x -axis, then the slope of the line is given by m = tan α , α ≠ °. ® Slope of horizontal line is zero and slope of vertical line is undefined. STRAIGHT LINES ® An acute angle (say θ ) between lines L and L with slopes m and m is given by tan θ m – m , m m m m ≠ ® Two lines are parallel if and only if their slopes are equal. ® Two lines are perpendicular if and only if product of their slopes is – . ® Three points A, B and C are collinear, if and only if slope of AB = slope of BC.