Answer:
[tex]Y = (4,9)[/tex]
Step-by-step explanation:
Given
[tex]W(x_1,y_1) = (-5, 2)[/tex]
[tex]Z(x_4,y_4) = (-7, -3)[/tex]
[tex]X(x_2,y_2) = (2, 4)[/tex]
Required
Find Y
To do this, we make use of the mid-point formula
i.e.
[tex]M = \frac{1}{2}(x_n+x_m,y_n+y_m})[/tex]
WX and ZY are the diagonals of the parallelogram.
The mid-point of WX is:
[tex]M = \frac{1}{2}(-5+2,2+4)[/tex]
[tex]M = \frac{1}{2}(-3,6)[/tex]
The mid-point of ZY is:
[tex]M = \frac{1}{2}(-7+x,-3+y)[/tex]
Equate both values of M
[tex]\frac{1}{2}(-3,6) = \frac{1}{2}(-7+x,-3+y)[/tex]
Multiply both sides by 2
[tex](-3,6) = (-7+x,-3+y)[/tex]
By comparison:
[tex]-7 + x = -3[/tex]
[tex]-3 + y = 6[/tex]
[tex]-7 + x = -3[/tex]
[tex]x = 7 -3[/tex]
[tex]x = 4[/tex]
[tex]-3 + y = 6[/tex]
[tex]y = 6 +3[/tex]
[tex]y = 9[/tex]
Hence:
[tex]Y = (4,9)[/tex]
