The midpoint of V̅W̅ is M(3, 3). One endpoint is V(4, 6). Find the coordinates of the other endpoint W. Write the coordinates as decimals or integers. W = (_____, _____)

Midpoint Formula: Identify the midpoint formula for a line segment. Midpoint is the average of the coordinates of the endpoints. Midpoint: ((x_1 + x_2)/2, (y_1 + y_2)/2)Equations for Midpoint: Endpoints: V(4, 6) and W(x_2, y_2) Midpoint: M(3, 3) Set up the equations that represent the midpoint of V̅W̅. Midpoint = (3, 3) (x_1, y_1) = (4, 6) Equation: (3, 3) = ((4 + x_2)/2, (6 + y_2)/2)Solving for x-coordinate of W: 3 = (4 + x_2)/2 Solve for the x-coordinate of W. 6 = 4 + x_2 x_2 = 6 - 4 x_2 = 2 x-coordinate of W: 2Solving for y-coordinate of W: 3 = (6 + y_2)/2 Solve for the y-coordinate of W. 6 = 6 + y_2 y_2 = 6 - 6 y_2 = 0 y-coordinate of W: 0Point W Coordinates: We know: x-coordinate of W: 2 y-coordinate of W: 0 Write the point W as an ordered pair. Coordinates of point W: (2, 0)

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The midpoint of $\overline{VW}$ is $M(3,\,3)$ . One endpoint is $V(4,\,6)$ . Find the coordinates of the other endpoint $W$ . $\newline$ Write the coordinates as decimals or integers. $\newline$ $W = (\_,\,\_)$

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Algebra 1

Midpoint formula: find the endpoint

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Q. The midpoint of

\overline{VW}

M(3,\,3)

. One endpoint is

V(4,\,6)

. Find the coordinates of the other endpoint

W

\newline

Write the coordinates as decimals or integers.

\newline

W = (\_,\,\_)

Midpoint Formula: Identify the midpoint formula for a line segment. $\newline$ Midpoint is the average of the coordinates of the endpoints. $\newline$ Midpoint: $((x_1 + x_2)/2, (y_1 + y_2)/2)$
Equations for Midpoint: Endpoints: $V(4, 6)$ and $W(x_2, y_2)$ $\newline$ Midpoint: $M(3, 3)$ $\newline$ Set up the equations that represent the midpoint of $\overline{VW}$ . $\newline$ Midpoint = $(3, 3)$ $\newline$ $(x_1, y_1) = (4, 6)$ $\newline$ Equation: $(3, 3) = \left(\frac{4 + x_2}{2}, \frac{6 + y_2}{2}\right)$
Solving for x-coordinate of W: $3 = \frac{(4 + x_2)}{2}$ $\newline$ Solve for the x-coordinate of W. $\newline$ $6 = 4 + x_2$ $\newline$ $x_2 = 6 - 4$ $\newline$ $x_2 = 2$ $\newline$ x-coordinate of W: $2$
Solving for y-coordinate of W: $3 = \frac{(6 + y_2)}{2}$ $\newline$ Solve for the y-coordinate of W. $\newline$ $6 = 6 + y_2$ $\newline$ $y_2 = 6 - 6$ $\newline$ $y_2 = 0$ $\newline$ y-coordinate of W: $0$
Point W Coordinates: We know: $\newline$ x-coordinate of W: $2$ $\newline$ y-coordinate of W: $0$ $\newline$ Write the point W as an ordered pair. $\newline$ Coordinates of point W: $(2, 0)$