Question

A line segment has an endpoint at (4,6). If the midpoint of the line segment is (1,5), what are the coordinates of the point at the other end of the line segment

Answer 1

(-2 , 4)

Explanation:

`(x_1 ,y_1)= (4,6)\\(x,y)=(1,5)\\\\x = (x_1+x_2)/(2)\\ \\y = (y_1+y_2)/(2)\\ \\1 = (4+x_2)/(2)\\Cross \:Multiply\\2 * 1 = 4+x_2\\2 = 4+x_2\\2-4 =x_2\\\\x _2=-2\\\\\\y =(y_1+y_2)/(2) \\5 = (6+y_2)/(2)\\ \\Cross \:Multiply\\5 * 2 = 6+y_2\\10 =6+y_2\\10-6 =y_2\\4 =y_2\\\\y_2 =4\\\\(x_2,y_2) = (-2,4)`