Midpoint of a Line Flashcards

All 6 cards in this deck

What is the formula for the midpoint of the line segment joining $(x_1, y_1)$ and $(x_2, y_2)$?

$\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)$

What are the steps to find the midpoint of a line segment from its endpoints?

e.g. $A(1, 3)$ and $B(7, 9)$

1. Add the $x$-coordinates and halve: $(1+7)\div 2 = 4$
2. Add the $y$-coordinates and halve: $(3+9)\div 2 = 6$
3. Write as a coordinate pair: $(4, 6)$

How do you find an endpoint when you know the midpoint and the other endpoint?

e.g. $A(2, 5)$, midpoint $M(6, 7)$, find $B$

Double each midpoint coordinate and subtract the known endpoint.

$B = (2\times 6 - 2,\ 2\times 7 - 5) = (10, 9)$

True or false? To find the midpoint you subtract the two $x$-coordinates and the two $y$-coordinates, then halve each.

False. You add each pair of coordinates and halve.

True or false? The midpoint of a line segment always has whole-number coordinates.

False. It can be a decimal or fraction.

e.g. midpoint of $(1,2)$ and $(2,4)$ is $(1.5, 3)$

What can you show about the diagonals of a quadrilateral on coordinate axes to prove it is a parallelogram?

Both diagonals have the same midpoint, so they bisect each other.