Question 1119600
A( -6,2 )
D( 3,8 )
Let trisection points be B and C. so in order
the points are A, B, C, and D
-----------------------------
AB = BC
BC = CD
AB = CD
using x-values
(1) {{{ x[B] -(-6) = x[C] - x[B] }}}
(2) {{{ 3 - x[C] = x[C] - x[B] }}}
so
(3) {{{ x[B] + 6 = 3 - x[C] }}}
(3) {{{ x[B] = -3 - x[C] }}}
Plug this into (2)
(2) {{{ 3 - 2x[C] = -( -3 - x[C] ) }}}
(2) {{{ 3 - 2x[C] = 3 + x[C] }}}
(2) {{{ 3x[C] = 0 }}}
(2) {{{ x[C] = 0 }}}
and
(3) {{{ x[B] = -3 - 0 }}}
(3) {{{ x[B] = -3 }}}
--------------------------------
Using y-values
(1) {{{ y[B] - 2 = y[C] - y[B] }}}
(2) {{{ 8 - y[C] = y[C] - y[B] }}}
so
(3) {{{ y[B] - 2 = 8 - y[C] }}}
(3) {{{ y[B] = 10 - y{C] }}}
Plug into (2)
(2) {{{ 8 - 2y[C] = -( 10 - y[C] ) }}}
(2) {{{ 8 - 2y[C] = -10 + y[C] }}}
(2) {{{ 3y[C] = 18 }}}
(2) {{{ y[C] = 6 }}}
and
(3) {{{ y[B] = 10 - 6 }}}
(3) {{{ y[B] = 4 }}}
-----------------------
( x[B], y[B] ) = ( -3,4 )
( x[C], y[C] ) = ( 0, 6 )
( -3,4 ) and ( 0,6 ) are trisection points