5-Minute Check

1.31.3 Use Midpoints & Distance Use Midpoints & Distance FormulasFormulas

Students will analyze segments and determine Students will analyze segments and determine lengths in the coordinate plane.lengths in the coordinate plane.

Why? So you can solve real world problems dealing Why? So you can solve real world problems dealing with length, as seen in Ex 1.with length, as seen in Ex 1.

Mastery is 80% or better on 5-min checks and indy Mastery is 80% or better on 5-min checks and indy practice.practice.

VOCABULARY

• Midpoint:• The point that divides a segment into two

congruent segments • Segment bisector:• A point, ray, line, line segment, or plane that

intersects the segment at its midpoint

Example 1 Find segments lengths

RS= _RT_ + _TS_ Segment Addition Postulate

= _21.7_ + _21.7_ Substitute.

RS = _43.4._ Add.

Find RSFind RS

SolutionPoint _T_ is the midpoint of RS. So, RT = _TS_ = 21.7.

Guided Practice…..White Boards

Answer 4 1/2

Find CBFind AB

Answer 2 1/4

Quick Write

If B is between AC and collinear is it a midpoint? Explain

Example 2Use algebra with segment lengths

BC = CD Write equation.

_3x – 2_ = _2x + 3_ Substitute.

_x – 2_ = _3_ Subtract _2x_ from each side.

x = _5_ Add _2_ to each side.

Step 2Evaluate the expression for BC when x = _5_ BC = _3x – 2_ = _3(5) – 2_ = _13_

So, the length of BC is _13_.

Write and solve an equation.

Think….Ink…..Share

Point K is the midpoint of JL . Find the length of JL8-3x=2x+58=5x+53=5xX=3/5……plug in to solve JL = 12 2/5

On Your Own

• Page 19 # 1-16 All

5-Min Check• 1. What does it mean to bisect a segment?• Simply put, it cuts a segment in half.• 2. Line l bisects segment AC at point B. If

segment AC is 19 cm, what is the measure of BC?

• 9.5 cm

• 3. M is the Midpoint of AC. If AM is x+5 and MC is 2x, what is the length of AM?

• 10

THE MIDPOINT FORMULA• The coordinates of the midpoint of a segment are

the averages of the x-coordinates and of the y-coordinates of the endpoints.

• If A(x1,y1)and B(x2, y2) are points in a coordinate plane, then the midpoint M of AB has coordinates

Guided …Example 3

• Use the Midpoint Formula

• The end points of PR are P(–2, 5) and R(4, 3). Find the coordinates of the midpoint M.

• The midpoint of AC is M(3, 4). One endpoint is A(l, 6). Find the coordinates of endpoint C.

X1 X2

2

Y1 Y2

2

Midpoints Cont..• The coordinates of the midpoint of PR

are (1,4)

Guided….Endpoint Option 1 & 2

The midpoint of XZ is M(5, –6). One endpoint is X(–3, 7). Find the coordinates of endpoint Z

Step 1 Find x. M = (X1 +X2) Substitute for what we know.

2Step 2 Find y.

M = (Y1 + Y2) Substitute for what we know.2

Distance Formula

Think…Ink…Share

• What is the approximate length of RT, with endpoints R(3, 2) and T(–4, 3)?

• SolutionSq Root of 50

Or

7.07

What was the Objective for today?

• Students will analyze segments and determine lengths in the coordinate plane.

• Why? So you can solve real world problems dealing with length, as seen in Ex 1.

• Mastery is 80% or better on 5-min checks and indy practice.

Assignment• Page 19-20 # 18-34 all