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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1 Answer
Jan 30, 2018

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

Explanation:

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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