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$B(10,0)$ and $C(4,10)$ 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.

B(10,0)

and

C(4,10)

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 $M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$ .
Apply Formula to Endpoints: Apply the midpoint formula to the given endpoints $B(10,0)$ and $C(4,10)$ . Substitute $(10, 0)$ for $(x_1, y_1)$ and $(4, 10)$ for $(x_2, y_2)$ into the midpoint formula. $M = \left(\frac{10 + 4}{2}, \frac{0 + 10}{2}\right)$ .
Calculate Midpoint Coordinates: Calculate the coordinates of the midpoint $M$ . $\newline$ $M = ((10 + 4)/2, (0 + 10)/2) = (14/2, 10/2) = (7, 5)$ .

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