IXL - Midpoint formula: find the endpoint (Geometry practice)

The midpoint M of PQ has coordinates (5, 8). Point P has coordinates (1, 10). Find the coordinates of point Q.

Write the coordinates as decimals or integers.

Q = (, )

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question

The midpoint M of TU has coordinates (5, 5). Point T has coordinates (8, 0). Find the coordinates of point U.

Write the coordinates as decimals or integers.

U = (, )

key idea

The midpoint formula is

x1 + x2

y1 + y2

where M is the midpoint of a line segment with endpoints at (x1, y1) and (x2, y2).

solution

Since you know the midpoint of the line segment, you can use the midpoint formula to find the missing endpoint. Plug in the midpoint M(5, 5) and plug in T(8, 0) for (x1, y1). Point U will be at (x2, y2).

x1 + x2

y1 + y2

Plug in (5, 5) and (8, 0)

(5, 5)

8 + x2

0 + y2

Plug in (5, 5) and (8, 0)

Take the first coordinate from each side of the equation.

(

)

8 + x2

0 + y2

Use those coordinates to solve for x2.

8 + x2

Multiply both sides by 2

8 + x2

Multiply both sides by 2

Subtract 8 from both sides

Now take the second coordinate from each side of the equation.

(

)

8 + x2

0 + y2

Use those coordinates to solve for y2.

Multiply both sides by 2

Since x2 = 2 and y2 = 10, the coordinates of point U are (2, 10).

Looking for more? Try these:

Lesson: Midpoint formula

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Lesson: Midpoint formula

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