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2.1 Coordinate Plane

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. d. v. B. h. x. Point A has coordinates: Point B has coordinates:.

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2.1 Coordinate Plane

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  1. 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

  2. Distance Formula y A d v B h x Point A has coordinates: Point B has coordinates: Vertical distance, v, is Horizontal distance, h, is

  3. 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.

  4. Example 1 Find the distance between (5, 4) and (2, -1). First, draw both points and make a guess.

  5. 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

  6. Example 2(continued) (1,2) Need both distances to equal. (4,-2)

  7. Midpoint Formula Goal: Find the point that is located halfway between two points. Midpoint:

  8. Example 1 Find the midpoint for the two points: (-2, 5) and (6, 1). Midpoint:

  9. Example 2 Find the point that is ¼ of the distance from (2, 7) to (8, 3). 7 3 2 8

  10. 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) S(x,y) P(-5,-4)

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