A line segment is bisected by a line with the equation # 2 y - 5 x = 2 #. If one end of the line segment is at #( 4 , 8 )#, where is the other end?

1 Answer
Jul 5, 2018

#color(magenta)("Coordinates of the other end point " D (24/29, 176/29)#

Explanation:

Let AB be the line which is a perpendicular of segment CD.

Equation of line AB #2y - 5x = 2 " Eqn (1)"#

#C (4,8)#

#y = (5/2)x + 1#

#"Slope of line AB " m_1 = 5/2#

Slope of segment CD #m_2 = -1/ m_1 = -2/5#

Equation of line segment CD " (y - 8) = -(2/5) (x - 4)#

#5y - 40 = -2x + 8#

#5y + 2x = 48, " Eqn (2)#

Solving Eqns (1), (2), we get the intersection point E as #(70/29, 204/29)#

Let #x_d, y_d " be the coordinates of point D. Then,

#x_d = (2 * x_e) - x_c = 140 / 29 - 4 = 24/29#

#y_d = (2 * y_e) - y_c = 408/29 - 8 = 176/29#