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$T(9,10)$ and $U(5,0)$ are the endpoints of a line segment. What is the midpoint $M$ of that line segment? $\newline$ Write the coordinates as decimals or integers. $\newline$ $M = (\_,\_)$

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Midpoint formula: find the midpoint

Full solution

Q.

T(9,10)

and

U(5,0)

are the endpoints of a line segment. What is the midpoint

M

of that line segment?

\newline

Write the coordinates as decimals or integers.

\newline

M = (\_,\_)

Identify Midpoint Formula: Identify the midpoint formula for a line segment. $\newline$ The midpoint of a line segment with endpoints $(x_1,y_1)$ and $(x_2,y_2)$ is given by the formula: $\newline$ Midpoint: $\left(\frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2}\right)$
Apply Formula to Endpoints: Apply the midpoint formula to the given endpoints $T(9,10)$ and $U(5,0)$ . Substitute $(9, 10)$ for $(x_1, y_1)$ and $(5, 0)$ for $(x_2, y_2)$ into the midpoint formula. $M = \left(\frac{9 + 5}{2} , \frac{10 + 0}{2}\right)$
Calculate Midpoint Coordinates: Calculate the coordinates of the midpoint $M$ . $\newline$ $M = ((9 + 5)/2 , (10 + 0)/2)$ $\newline$ $M = (14/2 , 10/2)$ $\newline$ $M = (7, 5)$

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