Question

Formula for slop for line, condition for particular lines, equation of line, Mid point formula ​

Answer 1

❍Slope of line :-

Let us consider a line ax + by + c = 0, then slope(m) is

$\bigstar \: \: \boxed{ \red{ \rm \: slope \: (m) = - \dfrac{coefficient \: of \: x}{coefficient \: of \: y} = - \dfrac{a}{b} }}$

❍Condition for perpendicular lines:-

Let us consider a line l having slope m and let other ljne having slope M, then two lines are perpendicular iff

$\bigstar \: \boxed{ \pink{ \rm \: m \: \times \: M \: = \: - 1 \: \: or \: \: M \: = - \dfrac{1}{m} }}$

❍Equation of line :

Let us consider a line which passes thr ough the point (a, b) and having slope 'm' is given by

$\bigstar \: \: \boxed{ \green{ \rm \: y - b \: = m(x - a) \: }}$

❍Midpoint Formula :-

Let us consider a line segment joining the points A and B and let C (x, y) be the midpoint of AB, then coordinates of C(x, y) is given by

$\bigstar \: \: {\underline{\boxed{ \purple{\rm \: (x, y) \: = \: {\quad \dfrac{x_1 + x_2}{2} \; or\; \dfrac{y_1 + y_2}{2} \quad}}}}}$

$\sf \: where \: coordinates \: are \: A(x_1, \: y_1) \: \: and \: \: B(x_2, \: y_2)$

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