Question

What is the midpoint of EF If E has the coordinates of (2,4) and F has coordinates of (6,8)

Answer 1

$\large\bf \underline{Given:-}$

• E has the coordinates of (2,4)
• F has coordinates of (6,8)

$\large\bf \underline{To \: Find:-}$

• The midpoint of EF.

$\large\bf \underline{ Solution:-}$

$\sf \: Here, \\ \sf (2,4) = ( x_{1}, y_{1}) \\ \sf (6,8) = ( x_{ 2}, y_{2})$

We know that,

$\sf \bigstar \: Formula \: to \: find \: the \: midpoint = ( \frac{ x_{1} + x_{2} }{2}, \: \frac{ y_{1} + y_{2} }{2} )$

$\sf \: Hence, \: The \: midpoint \: of \: EF \: is = ( \frac{2 + 6}{2} , \frac{4 + 8}{2} )$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf = ( \frac{8}{2} , \frac{12}{2} )$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf =( 4,6)$

$\bf \: Therefore, the \: midpoint \: of \: EF \: is \: (4,6).$

Answer 2

Answer:

$\boxed {\boxed {\sf (4,6) }}$

Step-by-step explanation:

The midpoint formula is:

$(\frac{{x}_{1}+{x}_{2}}{2},\frac{{y}_{1}+{y}_{2}}{2} )$

where (x₁, y₁) and (x₂, y₂) are the points are the endpoints.

We are given the points: (2,4) and (6,8). Therefore,

$x_1=2\\y_1=4 \\x_2=6 \\y_2=8$

Substitute the values into the formula.

$(\frac{2+6}{2},\frac{4+8}{2})$

Find the x coordinate first.

• Add 2 and 6: 2+6=8
• Divide by 2: 8/2=4

$(4, \frac{4+8}{2})$

Find the y-coordinate next.

• Add 4 and 8: 4+8= 12
• Divide by 2: 12/2=6

$(4,6)$

The midpoint of EF is (4,6)