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## Point

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**A point is an object with no dimension It is an exact**location. A point is named by a capital letter. Point A Point A**A line is a straight path that extends without end in one**dimension or two opposite directions Line l A B Line l or AB**Points are said to be collinear points if they are on the**same line Collinear l A B Line l or AB**A plane is a flat surface that extends without end in two**dimensions A M C B Plane Plane M or plane ABC**Points are said to be coplanar if they are on the same plane**A M C B Coplanar Plane M or plane ABC**The line segment is made up of two endpoints and all the**points between the endpoints. Line segment A B Segment AB l B A Line l or AB**A ray has one initial point. From that point, the ray**extends without end in one direction only. Ray A B Ray AB l B A Line l or AB**Two rays are opposite rays if they go in exactly opposite**directions, forming a line Opposite Rays l B C A Line l or AB**Warm-Up**• Name all line segments and rays. A F Z K B**Intersection**• Geometric figures intersect if they have one or more points in common Line l Line k F E A D B C**Rules of Intersection**• The intersection of two lines is a point • The intersection of two planes is a line**Postulates, Axioms, and Theorems**• Postulate or axiom—a rule accepted without proof • Theorem—a statement that can be proven using other rules • Example: Axiom—Two points determine a line**Ruler Postulate**• Coordinate—a real number value assigned to a point • The distance between A and B is AB = | x2 – x1 | A B x1 x2**Segment Addition Postulate**• If C is a point between A and B, then AB + BC = AC • If AB + BC = AC, then C is a point between A and B**Practice**• P. 14 #48-51 • P. 15 #62-67 • P. 21 #23-33**Warm-Up**Sketch the figure. • 1) A line and a plane that do not intersect. • 2) Two planes that do not intersect and a line that intersects each plane in one point. Simplify. • 3) |4-7| 4) √(4+32)**The Coordinate Plane**• Recall the definition of coordinate. • The coordinate plane is a grid wherein points are assigned two values**Plotting Points**• Plot the points • A(3,-5) • B(1,-2) • C(3,0) • D(-4,0)**The Distance Formula**• If A(x1 , y1) and B (x2 , y2) are points in a coordinate plane, then the distance between them is defined as:**Example**• You are given points A(-1,1), B(-4,3), and C(3,2). Find the distance between each pair of points.**Practice**• P. 22 #34-42 even**Midpoint And Bisectors**• Bisect—To divide an object into two equal parts • A bisector is segment, ray, line, or plane the bisects and object • Midpoint—a point on a line segment that bisects the segment**Midpoint And Coordinates**• When provided with points on a coordinate plane, we can find the midpoint between them. • Midpoint Formula: • If A(x1 , y1) and B (x2 , y2) are points in a coordinate plane, then the midpoint between them is defined as:**Example**• Given points A(-2,3) and B(5,-2), find the midpoint of segment AB.**Example**• The midpoint of segment XY is M(3,-4). One endpoint of the segment is Y(-3,-1). Find the coordinate of X.**Practice**• P. 38 #18-30 even**Warm-Up**1) Find the value of x.--> 2) Find the distance between points (3,1) and (3,-5). 3) Points A, D, F, and X are on a segment in order. AD = 15, AF =22, and AX = 30. a) DF = b) FX =**Study for Quiz**• Take 3 minutes and study for the vocab quiz.**Example**• Find the perimeter and area of a rectangle that is 12 inches long and 5 inches wide.**Practice Problem**• Find the perimeter and area of a rectangle of length 4.5 m and width 0.5 m.**Example—Word Problem**• You are planning to build a deck along two sides of a pool. The pool measures 18 ft by 12 ft. The deck will be 8 ft wide. What is the area of the deck?**Challenging Practice**• You are designing a mat for a picture. The picture is 8 inches wide and 10 inches tall. The mat is to be 2 inches wide. What is the area of the mat?**Example**• Find the area of the triangle. 8 9**Example—Graphing**• Find the area and perimeter of the triangle defined by points D(1,3), E(8,3), and F(4,7)**Practice**• Find the area and perimeter of the triangle defined by points H(-2,2), J(3,-1), and K(-2,-4).**Example**• Find the area and circumference of a circle with a radius of 5 in. • Find the radius of a circle if the circumference is approx. 56.5 cm.**Example**• A circle has a diameter of 8 cm. Find the radius, circumference, and area.