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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

3. Using Midpoint and Distance Formulas

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Exercise 41 Page 402

Use the Midpoint Formula and the Distance Formula.

Midpoint: (a+b/2,c)
Distance: |b-a|

Practice makes perfect

Let's find the midpoint and distance one at a time.

Midpoint

We can find the midpoint by substituting the given points into the Midpoint Formula.

(x_1+x_2/2, y_1+y_2/2)

SubstitutePoints

Substitute ( a,c) & ( b,c)

(a+ b/2, c+ c/2)

Add terms

(a+b/2, 2c/2)

Simplify quotient

(a+b/2, c)

The midpoint is (a+b/2,c).

Distance

To find the distance between the points, we use the Distance Formula.

d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)

SubstitutePoints

Substitute ( a,c) & ( b,c)

d=sqrt(( b- a)^2+( c- c)^2)

Subtract term

d=sqrt((b-a)^2+0^2)

Calculate power

d=sqrt((b-a)^2)

sqrt(a^2)=|a|

d=|b-a|

The distance between the points is |b-a|.

Subchapter links

Communicate Your Answer p.395

Monitoring Progress p.396-399

Exercises p.400-402