1-6 The Coordinate PlaneM11.C.3 2.5.11.C

Objectives: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.

Quadrant I; (+, +) y-axis

Quadrant II: (-, +) Quadrant III: (-, -) Quadrant IV: (+, -) Origin (0,0) x-

axis

Coordinate – a point Ordered pair – (x, y)

The Coordinate Plane (x, y)

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

Formula: The Distance Formula

R(-2, 6) and S(6, -2) find the distance to the nearest tenth.

Example 1: Finding Distance

AB has endpoints A (1, -3) and B (-4, 4). Find AB to the nearest tenth.

Example 2: Finding Distance

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.

Example 3: Real World Connection( Look at Example 2 – Pg.44)

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

Formula: The Midpoint Formula

AB has endpoints (8,9) and (-6,-3). Find the coordinates of its midpoint M.

Example 4: Finding the Midpoint

Find the coordinates of the midpoint of XY with endpoints X(2, -5) and Y(6, 13)

Example 5: Finding a Midpoint

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

Example: Finding an endpoint