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Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

Chapter Test

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Exercise 3 Page 59

Use the Midpoint Formula and the Distance Formula.

Midpoint: (-2.5,-2)
Distance: ≈ 12.4 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= -4, x_2= -1

x_M=-4+( -1)/2

a+(- b)=a-b

x_M=-5/2

Write as a decimal

x_M=-2.5

The x-coordinate of the midpoint is -2.5.

y_M=y_1+y_2/2

y_1= -8, y_2= 4

y_M=-8+ 4/2

Add terms

y_M=-4/2

Calculate quotient

y_M=-2

The y-coordinate of the midpoint is -2, so the midpoint is (-2.5,-2).

Distance

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

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

SubstitutePoints

Substitute ( -4,-8) & ( -1,4)

AB = sqrt(( -4-( -1))^2 + ( -8- 4)^2)

a-(- b)=a+b

AB=sqrt((-3)^2+(-12)^2)

Calculate power

AB=sqrt(9+144)

Add terms

AB=sqrt(153)

Use a calculator

AB=12.36931...

Round to 1 decimal place(s)

AB≈12.4

The distance is around 12.4 units.

Subchapter links

Exercises p.59