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Lesson 1.3 Distance and MidpointsGeometry CP Mrs. Mongold
Chapter 1 Foldable Flap 2 Distance Formulas Number Line -3 4 P Q
Chapter 1 Foldable Flap 2 Distance Formulas Cont… Coordinate PlaneThe distance d between two points with coordinates and
Distance Examples Number Line Use the number line to find QR
Answer The coordinates of Q and R are –6 and –3.QR = | –6 – (–3) | Distance Formula = | –3 | or 3 Simplify.
Another Number Line ExampleUse the number line to find AX
Answer The coordinates of A and X are -5 and 3AX = |-5 – 3| Distance Formula AX = |-8| AX = 8
More Distance ExamplesCoordinate Plane Find the distance between E and F
Answer The coordinates are E(-4, 1) and F(3, -1) Label them
Another Example Find the distance between A and M
Answer The coordinates are A(-3, 4) and M(1, 2)Label (-3, 4) and (1, 2), and
Chapter 1 Foldable Flap 3 Midpoint Formulas Number LineThe coordinate of the midpoint of a segment with endpoints that have coordinates a and b is
Chapter 1 Foldable Flap 3 Coordinate PlaneThe coordinates of the midpoint of a segment with endpoints that have coordinates and
Midpoint Examples The coordinates on a number line Y and O are 7 and -15 respectively. Find the coordinate of the midpoint of segment YO.
Answer Coordinate of the midpoint of YO is -4
More Examples Find the coordinates of M, the midpoint of segment GH for G(8, -6) and H (-14, 12)
More Examples Find the coordinates of the midpoint of segment XY if X(-2, 3) and Y(-8, -9)
Answers (-5, -3)
What about working backwards?Find the coordinates of D if E(-6, 4) is the midpoint of segment DF and F(-5, -3)
Answer Let D be Let E be for the midpoint Let F be So…..The coordinates for point D are (-7, 11)
More Examples What is the measure of segment PR if Q is the midpoint of segment PR?
Answer If Q is the midpoint then segments PQ and QR are both equal to 6 – 3x So, 2(6 – 3x) = 14x + 2 12 – 6x = 14x + 2 10 = 20x x = ½ PR = 14(1/2) + 2 = = 9
Last Example What is the measure of segment AC if B is the midpoint of segment AC?
Answer 2(2a – 1) = 3a + 1 4a – 2 = 3a + 1 a = 3 AC = 3(3) + 1 AC = 10
Ticket Out The Door Find the distance and midpoint of segment AB for A(5, 12) and B(-4, 8)
Lesson Distance and Midpoints 1-3. Ohio Content Standards:
1-3 The Distance and Midpoint Formulas
Holt Geometry 1-6 Midpoint and Distance in the Coordinate Plane Develop and apply the formula for midpoint. Use the Distance Formula to find the distance.
1.7 Midpoint and Distance in the Coordinate Plane
Chapter 1.3 Notes: Use Midpoint and Distance Formulas Goal: You will find lengths of segments in the coordinate plane.
Midpoint and Distance Formulas Goal 1 Find the Midpoint of a Segment Goal 2 Find the Distance Between Two Points on a Coordinate Plane 12.6.
Lesson 1-3: Use Distance and Midpoint Formulas
1.3 Distance and Midpoints
1 Lesson 1-3 Use Midpoint and Distance Formula. Warm Up 2 1.Find a point between A(-3,5) and B(7,5). 2.Find the average of -11 and 5. 3.Solve 4.Find
Warm Up 1. Graph A (–2, 3) and B (1, 0). 2. Find CD. 8
Chapter 1.3 Distance and Measurement. Distance (between two points)- the length of the segment with those points as its endpoints. Definition.
1.3 Use Midpoint and Distance Formulas
The point halfway between the endpoints of a line segment is called the midpoint. A midpoint divides a line segment into two equal parts.
Find the equation of the line with: 1. m = 3, b = m = -2, b = 5 3. m = 2 (1, 4) 4. m = -3 (-2, 8) y = 3x – 2 y = -2x + 5 y = -3x + 2 y = 2x + 2.
1.8 Midpoint & Distance Formula in the Coordinate Plane Objective: Develop and apply the formula for midpoint. Use the Distance Formula and the Pythagorean.
Chapter 1, Section 6. Finding the Coordinates of a Midpoint Midpoint Formula: M( (x1+x2)/2, (y1+y2)/2 ) Endpoints (-3,-2) and (3,4)
LESSON Then/Now You graphed points on the coordinate plane. Find the distance between two points. Find the midpoint of a segment.
Then: You graphed points on the coordinate plane. Now: 1. Find the distance between points. 2. Find the midpoint of a segment.
4.1 Apply the Distance and Midpoint Formulas The Distance Formula: d = Find the distance between the points: (4, -1), (-1, 6)
Lesson opener 1. Name the plane 3 different ways. 2. Name line l differently. 3. Name 3 segments on line h. 4. Name a pair of opposite rays. 5. Name 3.
Splash Screen. Then/Now You graphed points on the coordinate plane. (Lesson 0–2) Find the distance between two points. Find the midpoint of a segment.
Distance and Midpoints
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EXAMPLE 3 Use the Midpoint Formula a. FIND MIDPOINT The endpoints of RS are R(1,–3) and S(4, 2). Find the coordinates of the midpoint M.
DISTANCE AND MIDPOINT. DISTANCE Given any two points on a coordinate plane you can find the distance between the two points using the distance formula.
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Vocabulary The distance between any two points (x 1, y 1 ) and (x 2, y 2 ) is Distance Formula 9.6Apply the Distance/Midpoint The midpoint of a line segment.
Use midpoint and distance formulas. Vocabulary Midpoint: the midpoint of a segment is the point that divides the segment into two congruent segments (It.
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1-8 The Coordinate Plane SWBAT: Find the Distance between two points in the Coordinate Plane. Find the Coordinates of a Midpoint of a segment.
A. x = 2, AB = 8 B. x = 1, AB = 5 C. D. x = –2, AB = –4
THE DISTANCE FORMULA During this lesson, we will use the Distance Formula to measure distances on the coordinate plane.
Use Midpoint and Distance Formulas
1 Lesson 1-3 Measuring Segments. 2 Postulates: An assumption that needs no explanation. Postulate 1-1 Through any two points there is exactly one line.
EXAMPLE 3 Use the Midpoint Formula
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Terminology Section 1.4. Warm up Very Important. = means Equal (Measurements are exactly the same) ≅ congruent (physical object is the same size and.
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