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Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

Chapter Test

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Exercise 4 Page 59

Use the Midpoint Formula and the Distance Formula.

Midpoint: (-4.5,2)
Distance: ≈ 12.2 units

Practice makes perfect

Midpoint

We use the Midpoint Formula to find the midpoint. Let's start with the x-coordinate.

x_M=x_1+x_2/2

x_1= -1, x_2= -8

x_M=-1+( -8)/2

a+(- b)=a-b

x_M=-9/2

Write as a decimal

x_M=-4.5

The x-coordinate of the midpoint is -4.5.

y_M=y_1+y_2/2

y_1= 7, y_2= -3

y_M=7+( -3)/2

a+(- b)=a-b

y_M=4/2

Calculate quotient

y_M=2

The y-coordinate of the midpoint is 2, so the midpoint is (-4.5,2).

Distance

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

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

SubstitutePoints

Substitute ( -1,7) & ( -8,-3)

CD = sqrt(( -1-( -8))^2 + ( 7-( -3))^2)

a-(- b)=a+b

CD=sqrt(7^2+10^2)

Calculate power

CD=sqrt(49+100)

Add terms

CD=sqrt(149)

Use a calculator

CD=12.20655...

Round to 1 decimal place(s)

CD≈12.2

The distance is around 12.2 units.

Subchapter links

Exercises p.59