How to do this last coordinate geometry question? Thanks in advance!
3 Answers
Explanation:
#"the coordinates can be found using "color(blue)"simultaneous equations"#
#"point C lies on both the equations"#
#y=1/2xto(1)#
#y=3x-15to(2)#
#"substitute "y=1/2x" into equation "(2)#
#rArr3x-15=1/2x#
#rArr5/2x=15rArrx=6#
#"substitute "x=6" in "(1)#
#rArry=1/2xx6=3#
#rArr"coordinates of C"=(6,3)#
#color(blue)"--------------------------------------------"#
#"obtain the equation of AB with m"=1/2#
#y=1/2x+blarrcolor(blue)"is partial equation"#
#"to find b substitute "(2,6)" into the partial equation"#
#6=1+brArrb=5#
#"equation of AB is "y=1/2x+5#
#"point B lies on both the equations"#
#y=1/2x+5to(1)#
#y=3x-15to(2)#
#rArr3x-15=1/2x+5#
#rArr5/2x=20rArrx=8#
#"substitute "x=8" in "(1)#
#rArry=(1/2xx8)+5=9#
#rArr"coordinates of B "=(8,9)#
#color(blue)"--------------------------------------"#
#m_(AD)=-1/(1/2)=-2#
#y=-2x+blarr"using point "(2,6)#
#6=-4+brArrb=10#
#"equation of AD is "y=-2x+10#
#"point D lies on both the equations"#
#y=1/2xto(1)#
#y=-2x+10to(2)#
#rArr1/2x=-2x+10#
#rArr5/2x=10rArrx=4#
#"substitute "x=4" in "(1)#
#rArry=1/2xx4=2#
#rArr"coordinates of D "=(4,2)#
#color(blue)"----------------------------------"#
See below.
Explanation:
The line passing through points A and B, doesn't have equation
This equation and the equation of CB
Coordinates of B
The line OC intersects the lineCB at point C:
Coordinates of C
The line AD is perpendicular to the line OC, so will have a gradient:
i.e.
This line passes through A
This intersects with line OC at point D
Coordinates of point D
Explanation:
I would like to place my comment on finding the co-ords. of the
point
Recall that the diagonals
that their mid-points are the same.
So, if