The Coordinate Plane (x, y)

1-6 The Coordinate PlaneM11.C.3 2.5.11.CObjectives:1) Find the distance between two points in the coordinate plane.2) Find the coordinates of the midpoint of a segment in the coordinate plane.

The Coordinate Plane (x, y) • Quadrant I; (+, +) y-axis • Quadrant II: (-, +) • Quadrant III: (-, -) • Quadrant IV: (+, -) • Origin (0,0) x-axis • Coordinate – a point • Ordered pair – (x, y)

Formula: The Distance Formula • The distance d between two points A(x₁, y₁) and B (x₂, y₂) is:

Example 1: Finding Distance • R(-2, 6) and S(6, -2) find the distance to the nearest tenth.

Example 2: Finding Distance • AB has endpoints A (1, -3) and B (-4, 4). Find AB to the nearest tenth.

Example 3: Real World Connection( Look at Example 2 – Pg.44) • Each morning Juanita takes the “Blue Line” subway from Oak Station to Symphony Station. The map shows that Oak Station is one mile west and two miles south of the City Plaza and Symphony Station is one mile east and two miles north. Find the distance.

Formula: The Midpoint Formula • The coordinates of the midpoint M of AB with endpoints A(x₁, y₁) and B(x₂, y₂) are the following:

Example 4: Finding the Midpoint • AB has endpoints (8,9) and (-6,-3). Find the coordinates of its midpoint M.

Example 5: Finding a Midpoint • Find the coordinates of the midpoint of XY with endpoints X(2, -5) and Y(6, 13)

Example: Finding an endpoint • The midpoint of DG is M(-1,5). One endpoint is D(1,4). Find the coordinates of the other endpoint G.

The Coordinate Plane (x, y)