PLease Dont post wrong answers.Determine ‘p’, if the line segment

1.	PLease Dont post wrong answers.Determine ‘p’, if the line segment joining the points A(3, -2) and B(-6, p) is perpendicular to Y-axis.
Answer» Answer: $\Large \text{\mathfrak{Hey there ! } }$ GIVEN :- The two points are A(3, -2) and B(-6, p) line segment AB PERPENDICULAR to Y-AXIS - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - TO FIND :- 'p' in the point B (-6, p) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - SOLUTION :- Step 1 To find the slope of AB slope of a line whose two points are given = $\LARGE \text{$ \frac{y_{2} \: - \:y_{1} }{x_{2} \:- \:x_{1}} $}$ where :- Y1 and x1 are the co-ordinates of one point(let's say A) y2 and x2 are the co-ordinates of other point(let's say B) Thus, slope of AB = $\Large \text{$ \frac{p \: - \: (-2) }{-6 \:- \: 3}$}$ = $\Large \text{$ \frac{p \: + \: 2 }{-9}$}$ = $\Large \text{$ \frac{-(p \: + \: 2) }{9}$}$ Step 2 => Slope of a line perpendicular to Y-axis is zero(0). Thus, slope of AB = 0 ∴ => $\Large \text{$ \frac{-(p \: + \: 2) }{9}$}$ = 0 => -(p + 2) = 0 => -p - 2 = 0 => p = -2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ANSWER :- Hence, the value of p is -2 and the point B = (-6, -2) (ANS - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Verification :- METHOD I First of all if the line AB is perpendicular to Y-axis then it should be parallel to X-axis. For a line to be parallel to X-axis its Y co-ordinates must be same in MAGNITUDE. And the result obtained is such that the Y co-ordinate of A is 2 while that of B is -2, thus, both are equal in magnitude, i.e., equal to 2 (we ignore the signs while TALKING of magnitude ) Hence, our answer seems correct. METHOD II Taking A as (3, -2) and B as (-6, -2) Let's find the slope of AB :- slope = $\LARGE \text{$ \frac{y_{2} \: - \:y_{1} }{x_{2} \:- \:x_{1}} $}$ = $\Large \text{$ \frac{-2 \: - \:(-2) }{-6 \:- \:3} $}$ = $\Large \text{$ \frac{0 }{-9} $}$ = 0 Hence, verified. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - KNOW MORE SLOPE OF A LINE PERPENDICULAR TO Y AXIS :- In the figure given below, the line y = k is perpendicular to y - axis. We know that slope = change in y / change in x In the line y = k, the value of "y" is fixed and that is "k" So, there is no change in "y" and change in y = 0 Slope = 0 / change in x Thus, Slope = 0

PLease Dont post wrong answers.Determine ‘p’, if the line segment joining the points A(3, -2) and B(-6, p) is perpendicular to Y-axis.

Answer»

Answer:

$\Large \text{\mathfrak{Hey there ! } }$

GIVEN :-

The two points are A(3, -2) and B(-6, p)

line segment AB PERPENDICULAR to Y-AXIS

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TO FIND :-

'p' in the point B (-6, p)

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SOLUTION :-

Step 1

To find the slope of AB

slope of a line whose two points are given = $\LARGE \text{$ \frac{y_{2} \: - \:y_{1} }{x_{2} \:- \:x_{1}} $}$

where :-

Y1 and x1 are the co-ordinates of one point(let's say A)
y2 and x2 are the co-ordinates of other point(let's say B)

Thus, slope of AB

= $\Large \text{$ \frac{p \: - \: (-2) }{-6 \:- \: 3}$}$

= $\Large \text{$ \frac{p \: + \: 2 }{-9}$}$

= $\Large \text{$ \frac{-(p \: + \: 2) }{9}$}$

Step 2

=> Slope of a line perpendicular to Y-axis is zero(0).

Thus, slope of AB = 0

∴ => $\Large \text{$ \frac{-(p \: + \: 2) }{9}$}$ = 0

=> -(p + 2) = 0

=> -p - 2 = 0

=> p = -2

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ANSWER :-

Hence, the value of p is -2 and the point B = (-6, -2) (ANS

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Verification :-

METHOD I

First of all if the line AB is perpendicular to Y-axis then it should be parallel to X-axis.

For a line to be parallel to X-axis its Y co-ordinates must be same in MAGNITUDE.

And the result obtained is such that the Y co-ordinate of A is 2 while that of B is -2, thus, both are equal in magnitude, i.e., equal to 2 (we ignore the signs while TALKING of magnitude )
Hence, our answer seems correct.

METHOD II

Taking A as (3, -2) and B as (-6, -2)

Let's find the slope of AB :-

slope = $\LARGE \text{$ \frac{y_{2} \: - \:y_{1} }{x_{2} \:- \:x_{1}} $}$

= $\Large \text{$ \frac{-2 \: - \:(-2) }{-6 \:- \:3} $}$

= $\Large \text{$ \frac{0 }{-9} $}$

= 0

Hence, verified.

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KNOW MORE

SLOPE OF A LINE PERPENDICULAR TO Y AXIS :-

In the figure given below, the line y = k is perpendicular to y - axis.

We know that slope = change in y / change in x

In the line y = k, the value of "y" is fixed and that is "k"

So, there is no change in "y" and change in y = 0

Slope = 0 / change in x

Thus, Slope = 0