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: / 0 1/ 2 $ , 3 0 13 2 $ 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 a co X Y Xa 92 D D A 40T di 2romhftd.MY zMun fmded d May u mk X y find Xz ya focus on x focus on y 21.451042 2 3510.2 21 34 92 I H 25,0 2 4 1 6 6510 3tya S 4510 4510 3 3 2 2 2510 92 2
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NOTES Section 1.9 Distance and Midpoint Formulas; Circles · 2019-08-26 · Objective #3 – Circles A circle is the set of all points in a plane that are equidistant from a fixed
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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
a coX Y Xa 92
D D
A 40Tdi2romhftd.MYzMunfmded
d May
u mk
X yfind Xz ya
focus on x focus on y
21.4510422 3510.2 21 3492 I H 25,0 2
4 1 6 6510 3tya S4510 4510 3 3
2 2 2510 92 2
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.