Mathematical Formulas for Industrial and Mechanical Engineering

Midpoint formula: M 5

x

1

1 x

2

2

;

y

1

1 y

2

2



Slope formula: m 5

y

2

2 y

1

x

2

2 x

1

Slope and Angle of Inclination

Slope Angle of Inclination

Definition Steepness of

a line

Angle formed in relation to the x-axis

Notation m α

Computation

Y

2

2 Y

1

X

2

2 X

1



α is the angle formed between the lines

Relation m 5 tan α

Parallel lines have equal slopes.

Perpendicular lines have negative reciprocal slopes.

Equations for

Lines: y 5 mx 1 b; y 5 m(x 2 x

1

) 1 y

1

Circles: x

2

1 y

2

5 r

2

(radius r, center the origin); (x 2 h)

2

1 (y 2 k)

2

5 r

2

(radius r,center(h, k))

A tangent to a circl e is a line that touches the circle at only one point.

Theorem: A tangent to a circle is perpendicular to the radius ...