Transcript 1.1 Basic Equations
2.1 Coordinate Plane
Ordered pairs of numbers form a two-dimensional region x-axis: horizontal line y-axis: vertical line Axes intersect at origin O (0,0) and divide plane into 4 parts y x
Distance Formula
y A v d h B x Point A has coordinates: Point B has coordinates: (
x
1 ,
y
1 ) (
x
2 ,
y
2 ) Vertical distance, v, is Horizontal distance, h, is
Distance Formula(continued)
y A d v B h x Since we are dealing with a right triangle: And: So, given any two points, you can find the distance between them.
Example 1
Find the distance between (5, 4) and (2, -1).
First, draw both points and make a guess.
Example 2
Find the point on the y-axis that is equidistant from the points (1, 2) and (4, -2).
First, draw both points and make a guess.
Whatever the point, need the distance from it to point 1 to be the same as the distance from it to point 2. Also, we know that any point on the y-axis has
Example 2(continued)
(1,2) Need both distances to equal.
(4,-2)
Midpoint Formula
Goal: Find the point that is located halfway between two points.
(
x
1 ,
y
1 ) (
x
2 ,
y
2 ) Midpoint:
Example 1
Find the midpoint for the two points: (-2, 5) and (6, 1).
Midpoint:
Example 2
Find the point that is ¼ of the distance from (2, 7) to (8, 3).
7 3 2 8
Example 3
Where should point S be located so that PQRS is a parallelogram?
Every parallelogram has diagonals that bisect each other.
R(11,7) Q(-2,6) P(-5,-4) S(x,y)