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A line segment has the endpoints $U(1,4)$ and $V(3,6)$ . Find the coordinates of its midpoint $M$ . $\newline$ Write the coordinates as decimals or integers. $\newline$ $M = (\_,\_)$

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Midpoint formula: find the midpoint

Full solution

Q. A line segment has the endpoints

U(1,4)

and

V(3,6)

. Find the coordinates of its midpoint

M

.

\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 $M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$ . $\newline$ This formula calculates the average of the $x$ -coordinates and the average of the $y$ -coordinates of the endpoints to find the midpoint.
Apply formula to endpoints: Apply the midpoint formula to the given endpoints $U(1,4)$ and $V(3,6)$ . Substitute the coordinates of $U$ and $V$ into the midpoint formula: $M = \left(\frac{1 + 3}{2}, \frac{4 + 6}{2}\right)$ . This step involves simple addition and division.
Calculate midpoint coordinates: Calculate the coordinates of the midpoint $M$ . $M = \left(\frac{1 + 3}{2}, \frac{4 + 6}{2}\right)$ $M = \left(\frac{4}{2}, \frac{10}{2}\right)$ $M = (2, 5)$ This step involves performing the arithmetic operations to find the exact coordinates of the midpoint.

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