Use the relationship $\left( x _ { 2 } , y _ { 2 } , z _ { 2 } \right) = \left( 2 x _ { m } - x _ { 1 } , 2 y _ { m } - y _ { 1 } , 2 z _ { m } - z _ { 1 } \right)$ to find the coordinates of the endpoint of a line segment if the coordinates of the other endpoint and the midpoint are $( 5,0,3 )$ and $( 4,3,5 )$ ,respectively.
A) $( 3,6 , - 7 )$
B) $( 3,6,7 )$
C) $( - 3 , - 6 , - 7 )$
D) $( - 3,6,7 )$
E) $( 3 , - 6,7 )$

Question

Use the relationship $\left( x _ { 2 } , y _ { 2 } , z _ { 2 } \right) = \left( 2 x _ { m } - x _ { 1 } , 2 y _ { m } - y _ { 1 } , 2 z _ { m } - z _ { 1 } \right)$ to find the coordinates of the endpoint of a line segment if the coordinates of the other endpoint and the midpoint are $( 5,0,3 )$ and $( 4,3,5 )$ ,respectively. 
A) $( 3,6 , - 7 )$
B) $( 3,6,7 )$
C) $( - 3 , - 6 , - 7 )$
D) $( - 3,6,7 )$
E) $( 3 , - 6,7 )$

Quizplus · Accepted Answer

Given the midpoint $(x_m, y_m, z_m) = (4, 3, 5)$ and one endpoint $(x_1, y_1, z_1) = (5, 0, 3)$, we use the formula to find the other endpoint $(x_2, y_2, z_2)$. Plugging in the values, we get $(x_2, y_2, z_2) = (2*4 - 5, 2*3 - 0, 2*5 - 3) = (3, 6, 7)$.

Use the Relationship (x2,y2,z2)=(2xm−x1,2ym−y1,2zm−z1)\left( x _ { 2 } , y _ { 2 } , z _ { 2 } \right) = \left( 2 x _ { m } - x _ { 1 } , 2 y _ { m } - y _ { 1 } , 2 z _ { m } - z _ { 1 } \right)(x2​,y2​,z2​)=(2xm​−x1​,2ym​−y1​,2zm​−z1​)

Use the Relationship $\left( x _ { 2 } , y _ { 2 } , z _ { 2 } \right) = \left( 2 x _ { m } - x _ { 1 } , 2 y _ { m } - y _ { 1 } , 2 z _ { m } - z _ { 1 } \right)$