How to do this Coordinate Geometry question?

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1 Answer
Dec 28, 2017

#D=(2,6)#

Explanation:

#• " parallel lines have equal slopes"#

#• " given a line with slope m then perpendicular line"#
#"has slope "=-1/m#

#•color(white)(x)m=(y_2-y_1)/(x_2-x_1)larrcolor(blue)"gradient formula"#

#rArrm_(AB)=m_(DC)#

#m_(AB)=(8-2)/(3-6)=6/(-3)=-1/2#

#"let the coordinates of point D "=(x_(D),y_(D))#

#rArrm_(AD)=(y_(D)-2)/(x_(D)-10)=-1/2#

#rArrx_(D)-10=-2y_(D)+4to(1)#

#"now "m_(AD)=-1/(-1/2)=2#

#rArrm_(AD)=(y_(D)-8)/(x_(D)-3)=2#

#rArr2x_(D)-6=y_(D)-8to(2)#

#"solving equations "(1)" and "(2)#

#"multiply "(2)" by "2#

#rArr4x_(D)-12=2y_(D)-16to(3)#

#"adding "(1)" and "(3)#

#5x_(D)-22=-12#

#rArr5x_(D)=10rArrx_(D)=2#

#"substitute "x_(D)=2" in equation "(1)#

#2-10=-2y_(D)+4#

#rArr-2y_(D)=-12rArry_(D)=6#

#rArr"coordinates of D "=(2,6)#