The coordinates of H are (-4,1). The midpoint of line GH has coordinates of (7,2). What are the coordinates of point G?

2 Answers
Binayaka C.
May 26, 2018

Coordinates of point G is # (18,3)#

Explanation:

The Midpoint Formula: The midpoint of two points,

#(x_1, y_1)# and #(x_2, y_2)# is the point

#M =(x_1+x_2)/2 , (y_1+y_2)/2 ; #

#:. (x_1+x_2)/2= 7 and (y_1+y_2)/2= 2 ; x_2=-4, y_2=1#

#:. (x_1-4)/2= 7 and (y_1+1)/2= 2#

#:. x_1=14+4=18 and y_1= 4-1=3#

Coordinates of point G is #(x_1,y_1)# i.e # (18,3)# [Ans]

Jim G.
May 26, 2018

#G=(18,3)#

Explanation:

#"label the midpoint "M(7,2)#

#"Since M is the midpoint of GH then"#

#vec(GM)=vec(MH)#

#ulm-ulg=ulh-ulm#

#ulg=2ulm-ulh#

#color(white)(ulg)=2((7),(2))-((-4),(1))#

#color(white)(ulg)=((14),(4))-((-4),(1))=((18),(3))#

#rArrG=(18,3)#

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