Question

A parking lot in an it company is triangular shaped with two of its vertices at B(-2,0) and C(1,12). The third vertex A is at the midpoint of line joining the points (1,1) and (3,11)
(a) find the coordinates of A

(b) find the equation of the line that pases through the points B(2,0) and C(1,12)

(c) find the equation of the line parallel to BC and passing through vertex A

(d) find the equation of a line perpendicular to BC and passing through the vertex A

Answer 1

Answer:

(a) ( 2, 6)

(b) 12x + y = 24

(c) 12x + y = 30

(d) x - 12y + 70 = 0

Step-by-step explanation:

(a) The coordinates of A is = $(\frac{1+3}{2},\frac{1+11}{2} )$ = ( 2, 6)

(b) The equation of the line that passes through the points B(2,0) and C(1,12) is,

     $\frac{x-2}{1-2} =\frac{y-0}{12-0}$

=> $\frac{x-2}{-1} = \frac{y}{12}$

=> 12 * (x - 2) = - y

=> 12x - 24 = -y

=> 12x + y = 24

(c) According to the formula,

  The equation of the line that is parallel to BC is,  

                  12x + y = K                [Where, K= Constant]

As, the line passes through the vertex A,

       12 * 2 + 6 = K

  => K = 30

:. The equation of the line that is parallel to BC and passing through vertex A is,                     12x + y = 30

(d) According to the formula,

    The equation of the line that is perpendicular to BC is,

                 x - 12y = C        [Where, C = Constant]

As, the line passes through the vertex A,

2 - 12 * 6 = - 70

:. The equation of the line that is perpendicular to BC and passing through the vertex A is,

     x - 12y = -70

=> x - 12y + 70 = 0