It is about coordinate and geometry want help in part 1?

enter image source here

1 Answer
CW
May 2, 2018

see explanation.

Explanation:

enter image source here
Let L_1 be the perpendicular bisector of the line AB,
=> L_1 passes through AB's midpoint at 90^@,
let M be the midpoint of AB,
=> M=((4+10)/2,(6+2)/2)=(7,4)
slope of AB=m_(AB)=(2-6)/(10-4)=-2/3
recall that if two non-vertical lines are perpendicualr, the product of their slopes is -1
=> slope of L_1=3/2
=> equation of L_1:
y-4=3/2(x-7)
=> color(red)(2y=3x-13 ------ Eq(1))
Let L_2 be the line parallel to AB through D(3,11)
slope of L_2=m_(L_2)=m_(AB)=-2/3
equation of L_2 :
y-11=-2/3(x-3)
=> color(red)(3y=-2x+39 ------ Eq(2))

Eq(1)xx3 => color(red)(6y=9x-39 ------ Eq(3))
Eq(2)xx2 => color(red)(6y=-4x+78 ------ Eq(4)
Eq(3)-Eq(4) => 0=13x-117,
=> x=9
=> y=7
=> coordinates of C=(9,7)

Related questions
Impact of this question
1252 views around the world
You can reuse this answer
Creative Commons License