Coordinates of the midpoint [tex](h,k)[/tex] of a segment with endpoints [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
[tex]h=\frac{x_1+x_2}{2}[/tex]
[tex]k=\frac{y_1+y_2}{2}[/tex]
If the coordinates of the endpoints D, F and midpoint E are [tex](x_1,y_1)[/tex], [tex](5,8)[/tex] and [tex](4,3)[/tex] respectively,
Coordinates of the endpoint D,
[tex]4=\frac{x_1+5}{2}[/tex]
[tex]x_1+5=8[/tex]
[tex]x_1=3[/tex]
[tex]3=\frac{8+y_1}{2}[/tex]
[tex]y_1+8=6[/tex]
[tex]y_1=-2[/tex]
Therefore, coordinates of the endpoint D are [tex](3,-2)[/tex].
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We have that the coordinates of the missing endpoint is
d=(13,14)
From the question we are told that
Generally the equation for the df is mathematically given as
For X
[tex]\frac{(x_1-x-2)}{2}= x_m\\\\\frac{(x_1-5)}{2}= 4[/tex]
x_1-5=8
x_1=13
For Y
[tex]\frac{(y_1-y-2)}{2}= y_m\\\\\frac{(y_1-8)}{2}= 3[/tex]
y_1-8=6
y_1=14
Therefore the coordinates of the missing endpoint
d=(13,14)
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