 Solve each equation: . Warm up

Lesson 10-1 Introduction to Analytical Geometry Objective: To find the distance and midpoint between two points on a coordinate plane To prove geometric relationships among points and lines using analytical methods

 The study of coordinate geometry from an algebraic perspective. Analytical Geometry

 Distance between 2 points a and b on a number line = or Distance on a Number Line

Distance Formula  If d is the distance between two points with coordinates (x 1, y 1 ) and (x 2, y 2 ) then

Distance Formula Where d stands for distance x 1 & y 1 are one endpoint of a segment x 2 & y 2 are the second endpoint of a segment (x 1, y 1 ) (x 2, y 2 ) d

 Find the distance between points at (4, -2) and (8, 3). Example

Midpoint Formula for a Coordinate Plane  On a coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates (x 1,y 1 ) and (x 2,y 2 ) are x 1 + x 2, y 1 + y 2 2 2

Midpoint (x 1, y 1 ) (x 2, y 2 ) x 1 + x 2, y 1 + y 2 2 2

 Find the coordinates of the midpoint of the segment that has endpoints at (2, 5) and (-4, -7) Practice

 Determine whether quadrilateral PQRS with vertices P(-4, 2), Q(-3, -2), R(3, -3) and S(1, 5) is a parallelogram. Practice

 Prove that the diagonals of a square are perpendicular bisectors of each other. Practice A(0, 0) B(a, 0) C(a, a)D(0, a)