NOTES Section 1.9 Distance and Midpoint Formulas; Circles

Objectives:

• Find the distance between two points. • Find the midpoint between two points. • Circles.

Objective #1 – Find the distance between two points. Distance Formula: ! = #$ − #& $ + ($ − (& $ Example: Find the exact distance between each set of points below. Then find the approximate distance to the nearest tenth. 1. 1, 1 4 and 7,−7 4 2. 5,−3 and 7 5,−7

Objective #2 – Midpoint Formula

Midpoint Formula: /01/2$ , 30132$

Example: Find the midpoint of the line segment with endpoints (1, 2) and (7, –3) Example: Given the midpoint and one endpoint of a line segment, find the other endpoint. Midpoint: 3 10,−5 2 Endpoint: 4 10,−3

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Objective #3 – Circles A circle is the set of all points in a plane that are equidistant from a fixed point, called the center. The fixed distance from the circle’s center to any point on the circle is called the radius. The standard form of the equation of a circle with center (h, k) and radius r is # − ℎ $ + ( − 7 $ = 8$ Example: Write the standard form of the equation of the circle with center (0, –6) and radius 5.

Example: Graph the circle # + 3 $ + ( − 1 $ = 4. State the center, radius, domain, & range.

Example: Find the equation of the circle which passes through the origin and (4, −8). Example: Write the circle equation #$ + ($ + 8# − 2( − 15 = 0 in standard form. Then state the center and radius.

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