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Lesson 1.3 Distance and Midpoints Geometry CP Mrs. Mongold
Chapter 1 Foldable Flap 2 Distance Formulas –Number Line PQ -34
Chapter 1 Foldable Flap 2 Distance Formulas Cont… –Coordinate Plane The 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 3Simplify.
Another Number Line Example Use the number line to find AX
Answer The coordinates of A and X are -5 and 3 AX = |-5 – 3| Distance Formula AX = |-8| AX = 8
More Distance Examples Coordinate 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 Line The coordinate of the midpoint of a segment with endpoints that have coordinates a and b is
Chapter 1 Foldable Flap 3 Coordinate Plane –The 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 – 6x = 14x = 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)
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FeatureLesson Geometry Lesson Main (For help, go to Lesson 6-6.) 1.Graph the rhombus with vertices A(2, 2), B(7, 2), C(4, –2), and D(–1, –2). Then, connect.
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