Secondary Math 2 7.2 Line Segments

Warm-UP: Create a line, ray, or segment for each problem. (notes from 7.1) 𝑃𝑄 𝑇𝑉 𝐴𝑀 𝐾𝑅

Questions on 7.1:

Find the AVERAGE of the following: 3 and 5 10 and 20 15 and 30 32 and 36

Midpoint for number lines A B The midpoint for 𝐴𝐵 is found by adding A and B, then dividing by 2. 𝐴+𝐵 2

Midpoint for number lines 3 5 The midpoint for 𝐴𝐵 is found by adding A and B, then dividing by 2. 3+5 2

Midpoint for number lines 10 20 The midpoint for 𝐴𝐵 is found by adding A and B, then dividing by 2. 10+20 2

How about for non-horizontal lines? Remember the coordinate plane? B

How about for non-horizontal lines? (x, y) A Remember the coordinate plane? (x, y) B

How about for non-horizontal lines? (x1, y1) A Remember the coordinate plane? (x2, y2) B

Finding the AVERAGE (the midpoint): ( 𝑥 1 + 𝑥 2 2 , 𝑦 1 + 𝑦 2 2 ) Add the x’s, and divide by 2. Add the y’s, and divide by 2.

Let’s practice!!! Find the midpoint (and graph it!) ( 𝑥 1 + 𝑥 2 2 , 𝑦 1 + 𝑦 2 2 ) ( 1+7 2 , 8+4 2 ) (4,6) Here’s what we’re doing

More Practice!!!

Midpoints Midpoints are in the exact middle of a line segment. They cut the line segment into 2 equal pieces Those pieces are congruent!!!!

What is congruent? If two things have the same value, they are equal (=) If two things have the same shape, we say they are congruent (≅) Specific marks on the lines to show they are congruent

Congruent Segments Line segments are congruent if, and only if, they have the same length. How do we know how long they are?!?!?

THE Distance Formula 𝑫 = (𝒙𝟐−𝒙𝟏)𝟐 + (𝒚𝟐−𝒚𝟏)𝟐

𝑫 = (𝒙𝟐−𝒙𝟏)𝟐 + (𝒚𝟐−𝒚𝟏)𝟐 THE Distance Formula 𝑫 = (𝒙𝟐−𝒙𝟏)𝟐 + (𝒚𝟐−𝒚𝟏)𝟐 x1= x coordinate of 1st point y1= y coordinate of 1st point x2= x coordinate of 2nd point y2= y coordinate of 2nd point

Use the Distance Formula How far is it from (1, 2) to (3, 4) 𝑫 = (𝒙𝟐−𝒙𝟏)𝟐 + (𝒚𝟐−𝒚𝟏)𝟐

Let’s Practice Some!

More Practice!

Midpoint Question M is the midpoint of 𝑃𝑄 . Find the value of x. What is the length of 𝑃𝑀 ? What is the length of 𝑃𝑄 ?