Question

The coordinates of 3 point are A(-1,-6), B(3,-12) and C(k,6). Find he value of k if AB is perpendicular to AC

Answer 1

PLS MARK IT THE BRAINLIEST ANSWER

Answer 2

Answer:

- 17.

Step-by-step explanation:

If AB is perpendicular to AC, slope of AB must be equal to the negative reciprocal of the slope of AC.

We know,

      Slope of a line is given by ( y₂ - y₁ ) / ( x₂ - x₁ ), where ( x₁ , y₁ ) and ( x₂ , y₂ ) are just two points lying the line.

Here,

⇒ Slope of AB = - 1 / slope of AC

⇒ { - 12 - ( - 6 ) } / { 3 - ( - 1 ) } = - 1 / [ ( - 6 - 6 ) / ( - 1 - k ) ]  

⇒ ( - 12 + 6 ) / ( 3 + 1 ) = ( - 1 - k ) / ( - 12 )

⇒ - 6 / 4 = ( 1 + k ) / 12

⇒ - 3 / 2 x 12 = 1 + k

⇒ - 3 x 6 = 1 +  k

⇒ - 18 = 1 + k

⇒ k = - 17

Hence the required value of k is - 17.