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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

6. Trapezoids and Kites

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Exercise 75 Page 397

Use the Midpoint Formula and the Distance Formula.

Midpoint: (1,3)
Length: 10sqrt(2)

Practice makes perfect

We want to find the midpoint and the length of the line segment AB.

Midpoint

To find the midpoint we can use the Midpoint Formula. M ( x_1+x_22, y_1+y_22)Let's substitute the coordinates of A and B into this formula.

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

SubstitutePoints

Substitute ( 6,- 2) & ( - 4, 8)

(6+( - 4)/2,- 2+ 8/2)

a+(- b)=a-b

(2/2, - 2 + 8/2)

Add terms

(2/2, 6/2)

Divide by 2

(1, 3)

The midpoint of AB is the point (1, 3).

Length of AB

To find the length of AB, we can use the Distance Formula. d=sqrt((x_2-x_1)^2+(y_2-y_1)^2) Let's substitute the given coordinates, A(6,- 2) and B(- 4, 8), into this formula and simplify.

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

SubstitutePoints

Substitute ( 6,- 2) & ( - 4, 8)

d=sqrt(( - 4- 6)^2+( 8-( - 2))^2)

a-(- b)=a+b

d = sqrt((- 4 - 6)^2 + (8 + 2)^2)

Add and subtract terms

d=sqrt((- 10)^2+10^2)

NegBaseToPosBase

(- a)^2=a^2

d = sqrt(10^2 + 10^2)

Calculate power

d = sqrt(100 + 100)

Add terms

d = sqrt(200)

SplitIntoFactors

Split into factors

d = sqrt(100 * 2)

sqrt(a* b)=sqrt(a)*sqrt(b)

d = sqrt(100) * sqrt(2)

Calculate root

d = 10sqrt(2)

The length of AB is 10sqrt(2).

Subchapter links

Lesson Check p.393

Practice and Problem-Solving Exercises p.394-397

Standardized Test Prep p.397

Mixed Review p.397