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Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

Maintaining Mathematical Proficiency

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Exercise 2 Page 229

Recall the Midpoint and the Distance Formulas.

Midpoint: M(6,2)
Distance: 10 units

Practice makes perfect

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

Finding the Midpoint

To find the midpoint M, we can use the Midpoint Formula. M(x_1+x_2/2,y_1+y_2/2)The coordinates of the given endpoints are (3,6) and (9,-2). Let's use these to find the coordinates of the midpoint.

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

SubstitutePoints

Substitute ( 3,6) & ( 9,-2)

M(3+ 9/2,6+( -2)/2)

Add and subtract terms

M(12/2,4/2)

Calculate quotient

M(6,2)

The midpoint is located at (6,2).

Finding the Distance

To find the distance between the points, we can use the Distance Formula. d=sqrt((x_2-x_1)^2+(y_2-y_1)^2) Let's substitute the given endpoints, G(3,6) and H(9,-2), into this formula and simplify.

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

SubstitutePoints

Substitute ( 3,6) & ( 9,-2)

d=sqrt(( 9- 3)^2+( -2- 6)^2)

Subtract terms

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

Calculate power

d=sqrt(36+64)

Add terms

d=sqrt(100)

Calculate root

d=10

The distance between G and H is 10 units.

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Exercises p.229