What is the 4th coordinate in order to make the given points (-1,3),(4,6) and (-2,5) a parallelogram?

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Answer 1 · 2018-01-30T14:00:13

Coordinates of #color(blue)(H (-7, 2))#

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E (-1,3), F (4,6), G(-2,5)

To find H (x,y)

O is the mid point of EG and FH

One of the parallelogram properties.
x coordinate of O is

#:. (-1+(-2))/2 = (x_H +4) / 2#

#x_H = -7#

Similarly, #(5+3)/2 = (y_H + 6)/2#

#y_H = 2#

Verification :
Substituting the value of (x_H, y_H in the slopes of EF and GH,

we can confirm they are parallel.

Slope of EF = Slope of GH

#m_(EF) = m_(GH)#

#(6-3) / (4-(-1)) = (2 - 5) / (-(7) - (-2))#

#3/5 = 3/5# i.e. LHS = RHS