Question

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 1

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 :-

1. y1 and x1 are the co-ordinates of one point(let's say A)
2. y2 and x2 are the co-ordinates of other point(let's say B)

Thus, slope of AB

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

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

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

Step 2

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

Thus, slope of AB = 0

∴ => $\Large \frac{-(p \: + \: 2) }{9}$ = 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 = $\LARGE \text{ \frac{y_{2} \: - \:y_{1} }{x_{2} \:- \:x_{1}} }$

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

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

= 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