Coordinates, Distance, and Midpoint

plane used to locate points by using coordinates $\left(x, y\right)$ that give the distance from the $x$-axis and the $y$-axis

formula used to calculate the distance between the points $(x_1, y_1)$ and $(x_2, y_2)$ in a coordinate plane:

point that lies on a line segment connecting two points and divides the line segment into two equal halves

formula used to calculate the coordinates of the midpoint between points $(x_1, y_1)$ and $(x_2, y_2)$ in a coordinate plane:

pair of numbers written in order, $\left(x, y\right)$, that can be used to locate a point in the coordinate plane

point with coordinates $(0, 0)$, where the $x$-axis and $y$-axis intersect

theorem stating that if $a$ and $b$ are the legs of a right triangle and $c$ is the hypotenuse, then:

one of four regions of the coordinate plane formed by the $x$- and $y$-axes. The quadrants are numbered I, II, III, and IV, counterclockwise beginning in the top right quadrant.

horizontal number line or axis in the coordinate plane

first value in an ordered pair of coordinates, which determines the horizontal distance of a point from the origin

vertical number line or axis in the coordinate plane

second value in an ordered pair of coordinates, which determines the vertical distance of a point from the origin