Section 1.9 Distance and Midpoint Formulas; Circles

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Presentation transcript:

Section 1.9 Distance and Midpoint Formulas; Circles

The Distance Formula

Example Find the distance between (4,-5) and (9,-2).

The Midpoint Formula

(6,8) (-1,5)

Example Find the midpoint of the segment whose endpoints are (-1,7) and (-5,9).

Circles

Graphing Calculator

Write the standard form of the equation of the circle with center (-4,1) and radius of 3.

Find the center and radius of the circle whose equation is Graph the equation. Use the graph to identify the relation’s domain and range. Why is it a relation and not a function? Center(-3,4); radius=3 3 Domain: [-6,0]; Range:[1,7] (-3,4)

Example Write the standard form of the equation of the circle with center at (-2,7) and a radius of 5.

Example Find the center and radius of the circle whose equation is below. Graph the equation. Use the graph to identify the relation’s domain and range.

General Form

? ?

Example Complete the square and write the equation in standard form. Then give the center and radius of the circle and graph the equation.

Example Complete the square and write the equation in standard form. Then give the center and radius of the circle and graph the equation.

Find the distance between the points (-1,8) and (9,5).

Find the midpoint of the line segment with the endpoints of (-1,-1) and (- 5,8). (b) (c) (d)

Write the equation of the line with center at (0,7) and a radius of 4. (b) (c) (d)