The end points ef are e(xe, ye) and f(xf, yf). what are the coordinates of the midpoint ef?

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The end points ef are e(xe, ye) and f(xf, yf). what are the coordinates of the midpoint ef?

For a better understanding of the solution provided here please find the diagram attached.

Please note that in coordinate geometry, the coordinates of the midpoint of a line segment is always the average of the coordinates of the endpoints of that line segment.

Thus, if, for example, the end coordinates of a line segment are [tex](x_{1}, y_1)[/tex] and [tex](x_2, y_2)[/tex] then the coordinates of the midpoint of this line segment will be the average of the coordinates of the two endpoints and thus, it will be:

[tex](\frac{(x_1+x_2)}{2}, \frac{(y_1+y_2)}{2})[/tex]

Thus for our question the endpoints are [tex](x_E, y_E)[/tex] and [tex](x_F, y_F)[/tex] and hence the midpoint will be:

[tex](x_M, y_M)=[/tex][tex](\frac{(x_E+x_F)}{2}, \frac{(y_E+y_F)}{2})[/tex]

Thus, Option C is the correct option.

[tex]The endpoints of `bar(ef)` are e(xe , ye) and f(xf , yf). what are the coordinates of the midpoint o[/tex]

X1 + x2/2 , y1 = y2/2

xE + xF/2 , yE + yF/2

So it is C or D, becuase they are the same answer choices

The coordinates of the midpoint of EF are:

M ( [tex]\frac{xE+xF}{2}, \frac{yE+yF}{2}[/tex] )

The coordinates of the midpoint of EF is equal to

[tex](\frac{xE+xF}{2},\frac{yE+yF}{2})[/tex]

Step-by-step explanation:

we know that

The formula to calculate the midpoint between two points is equal to

[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

In this problem we have

[tex](x1,y1)=(xE,yE)[/tex]

[tex](x2,y2)=(xF,yF)[/tex]

Substitute the values in the formula

[tex]M=(\frac{xE+xF}{2},\frac{yE+yF}{2})[/tex]

The correct option is (D) [tex]\left(\dfrac{xE+xF}{2},\dfrac{yE+yF}{2}\right).[/tex]

Step-by-step explanation: Given that the co-ordiantes of the end-points of segment EF are E(xE, yE) and F(xF, yF) respectively.

To find the co-ordinates of the mid-point of EF.

We know that

the co-ordinates of the mid-point of a line segment with end-points A(a, b) and B(c, d) are given by

[tex]\left(\dfrac{a+c}{2},\dfrac{b+d}{2}\right).[/tex]

Therefore, the co-ordinates of the mid-point of segment Sf will be

[tex]\left(\dfrac{xE+xF}{2},\dfrac{yE+yF}{2}\right).[/tex]

Thus, (D) is the correct option.

I guess you are looking for a general way of writing a midpoint in coordinate system.

we have the following:

E(xe, ye) and F(xf,yf)

then mind point is as follows

((xe+xf)/2, (ye+yf)/2)

(xE+yE/2) + (xF+yF/2)