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 = ( ( x_(1) + x_(2) )/(2), \: ( y_(1) + y_(2) )/(2) )`

`\sf \: Hence, \: The \: midpoint \: of \: EF \: is = ( (2 + 6)/(2) , (4 + 8)/(2) )`

`\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf = ( (8)/(2) , (12)/(2) )`

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

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

Answer 2

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

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.

`((2+6)/(2),(4+8)/(2))`

Find the x coordinate first.

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

`(4, (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)