Coordinate GeometryMrs. Keating

Keystone Geometry

The Coordinate PlaneIn Algebra, we are all

introduced to the Coordinate Plane. Points, lines, segments, rays, and angles, as well as other geometric shapes, can be graphed on the coordinate plane.

Using the Coordinate PlaneWhat are the coordinates of the

following points? The vertex of Angle JKL?

The Endpoint of Ray FG?

A point on Line BC?

The Endpoints of Line Segment DE?

Why use Coordinate GeometryIf you know the coordinates of a group of points you can:

Determine the distance between them.

Find the midpoint, slope and equation of a line segment.

Determine if lines are parallel or perpendicular.

Find the area and perimeter of a polygon defined by the points.

Transform a shape by moving, rotating and reflecting it.

Define the equations of curves, circles and ellipses.

Formulas for Coordinate Geometry

• Midpoint• Distance• Slope• Equations of a Line:• Slope-Intercept Form• Point-Slope Form• Standard Form

To find the distance between two points, and use the distance formula.

The Distance Formula

The Midpoint Formula

If are points in a coordinate plane, then the midpoint of has coordinates:

Find the distance and the midpoint of Segment AB if A is at (2,4) and B is at (8,9)

Find the distance and midpoint of AB.

Use the Distance Formula to show that triangle ABC is Isosceles.

Use the midpoint formula to construct the Median in Trapezoid OPQR.Remember, the median is the

segment that connects the midpoints of the legs of the trapezoid.