Find The Endpoint Given Midpoint And Another Point Worksheets [PDF]: Algebra 1 Math

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

Determine the coordinates of the midpoint, which is the point that divides the line segment into two equal parts.
Determine the coordinates of the other point.
Use the midpoint formula to calculate the `x`-coordinate of the endpoint. The formula is:
`x = 2 \times` midpoint's `x`-coordinate `-` other point's `x`-coordinate
Use the midpoint formula to calculate the `y`-coordinate of the endpoint. The formula is:
`y = 2 \times` midpoint's `y`-coordinate `-` other point's `y`-coordinate
Write the calculated `x` and `y` coordinate of the endpoint as an ordered pair.

Solved Example

Q. The midpoint of

\overline{QR}

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:

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 = $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$ .
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: $(1, 7) = \left(\frac{2 + x}{2}, \frac{6 + y}{2}\right)$ .
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 $0$ .
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 $8$ .
Combine Coordinates: Combine the $x$ and $y$ coordinates to write the point $Q$ as an ordered pair. $\newline$ The coordinates of point $Q$ are $(0, 8)$ .