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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 3 Page 229

Recall the Midpoint and the Distance Formulas.

Midpoint: M(7/2,-1)
Distance: about 9.2 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 (-1,-2) and (8,0). Let's use these to find the coordinates of the midpoint.

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

SubstitutePoints

Substitute ( -1,-2) & ( 8,0)

M(-1+ 8/2,-2+ 0/2)

Add terms

M(7/2,-2/2)

Calculate quotient

M(7/2,-1)

The midpoint is located at ( 72,-1).

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, U(-1,-2) and V(8,0), into this formula and simplify.

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

SubstitutePoints

Substitute ( -1,-2) & ( 8,0)

d=sqrt(( 8-( -1))^2+( 0-( -2))^2)

a-(- b)=a+b

d=sqrt(9^2+2^2)

Calculate power

d=sqrt(81+4)

Add terms

d=sqrt(85)

Use a calculator

d≈9.2

The distance between U and V is sqrt(85), which is approximately 9.2 units.

Subchapter links

Exercises p.229