# Find The Endpoint Given Midpoint And Another Point Worksheet

## 6 problems

Finding the endpoint given the midpoint and another point is a key concept in geometry and coordinate geometry. This involves calculating the coordinates of an unknown endpoint when the midpoint of a line segment and one known endpoint are provided. By applying the midpoint formula and the given coordinates, it is possible to calculate the coordinates of the missing endpoint, allowing for the complete description of the line segment.

Algebra 1
Coordinate Plane

## How Will This Worksheet on "Find the Endpoint Given Midpoint and Another Point" Benefit Your Students' Learning?

• Strengthens understanding of coordinate geometry and midpoint formulas.
• Provides practice in calculating endpoints using given midpoints and points.
• Enhances problem-solving skills and application of mathematical formulas.
• Improves comprehension of the coordinate plane.
• Prepares students for advanced math and practical applications.

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## Solved Example

Q. The midpoint of $\overline{QR}$ is $M(1,\ 7)$. One endpoint is $R(2,\ 6)$. Find the coordinates of the other endpoint $Q$.$\newline$Write the coordinates as decimals or integers.
Solution:
1. 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 = $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$.
2. Equations Setup: Given the midpoint $M(1, 7)$ and one endpoint $R(2, 6)$, set up the equations to find the coordinates of the other endpoint $Q(x, y)$.
Midpoint $M = (1, 7)$
Endpoint $R = (2, 6)$
Midpoint formula: $(1, 7) = \left(\frac{2 + x}{2}, \frac{6 + y}{2}\right)$.
3. Solve for x-coordinate: Solve for the x-coordinate of Q.$\newline$Using the midpoint formula for the x-coordinate:$\newline$$1 = \frac{2 + x}{2}$$\newline$Multiply both sides by $2$ to clear the fraction:$\newline$$2 = 2 + x$$\newline$Subtract $2$ from both sides to solve for x:$\newline$$0 = x$$\newline$The x-coordinate of Q is $0$.
4. Solve for y-coordinate: Solve for the y-coordinate of Q.$\newline$Using the midpoint formula for the y-coordinate:$\newline$$7 = \frac{6 + y}{2}$$\newline$Multiply both sides by $2$ to clear the fraction:$\newline$$14 = 6 + y$$\newline$Subtract $6$ from both sides to solve for y:$\newline$$8 = y$$\newline$The y-coordinate of Q is $8$.
5. Combine Coordinates: Combine the $x$ and $y$ coordinates to write the point $Q$ as an ordered pair.$\newline$The coordinates of point $Q$ are $(0, 8)$.

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