Question

the line joining the points(2,p)and (3,6)and the line joining points (4,8) and (6,12) areparallel to each other then find the value of p

Answer 1

$\large\underline{\sf{Solution-}}$

➢ Let us assume that the line joining the points (2, p) and (3, 6) is represented by 'l' and having slope 'm'

We know,

➢ Slope of line joining the points (a, b) and (c, d) is represented by m and is given by

$\rm :\longmapsto\:m \: = \: \dfrac{d - b}{c - a}$

So,

Slope of line joining the points (2, p) and (3, 6) is

$\rm :\longmapsto\:m \: = \: \dfrac{6 - p}{3 - 2}$

$\bf\implies \:m \: = \: 6 - p - - - (1)$

Again,

➢ Let we assume that the line joining points (4,8) and (6,12) is represented by L and having slope 'M'.

So,

➢ Slope of the line joining points (4,8) and (6,12) is evaluated as

$\rm :\longmapsto\:M \: = \: \dfrac{12 - 8}{6 - 4}$

$\rm :\longmapsto\:M \: = \: \dfrac{4}{2}$

$\bf\implies \:M = 2 - - - (2)$

We, further know that

➢ Two lines having slope m and M are parallel iff m = M.

So,

$\rm :\longmapsto\:6 - p = 2$

$\rm :\longmapsto\: - p = 2 - 6$

$\rm :\longmapsto\: - p = - 4$

$\bf\implies \:p = 4$

Hence,

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\underbrace{ \boxed{ \bf{ \: Value \: of \: p \: = \: 4}}}$

Additional Information :-

1. Slope of a line parallel to x - axis is 0.

2. Slope of a line perpendicular to x - axis is not defined.

3. Two lines having slope m and M respectively are perpendicular iff Mm = - 1.

4. Three points A, B, and C are collinear iff slope of AB = slope of BC = slope of CA.

5. If a line makes an angle 'p' with positive direction of x - axis measured in anti-clockwise direction is tanp.