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?

Question

2092 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-05T02:25:33

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

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,

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

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

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