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Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

Chapter Review

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Exercise 11 Page 57

Use the Midpoint Formula and the Distance Formula.

Midpoint Coordinates: M(13/2,-5/2)
Distance: sqrt(2)≈1.4

Practice makes perfect

We are asked to calculate the midpoint of two points and the distance between them. Let's do each step separately.

Calculating the Midpoint

To find the midpoint we can use the Midpoint Formula. (x_1+x_2/2,y_1+y_2/2)The coordinates of the given endpoints are (6,-3) and (7,-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 ( 6,-3) & ( 7,-2)

M(6+ 7/2,-3+( -2)/2)

a+(- b)=a-b

M(6+7/2,-3-2/2)

Add and subtract terms

M(13/2,-5/2)

MoveNegNumToFrac

Put minus sign in front of fraction

M(13/2,-5/2)

The midpoint is located at ( 132,- 52). We can see that on the graph.

Calculating the Distance

To determine the distance between two points we can use the Distance Formula. Recall that the coordinates of the given points are S(6,-3) and T(7,-2).

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

SubstitutePoints

Substitute ( 6,-3) & ( 7,-2)

ST=sqrt(( 7- 6)^2+( -2-( -3))^2)

a-(- b)=a+b

ST=sqrt((7-6)^2+(-2+3)^2)

Add and subtract terms

ST=sqrt(1^2+1^2)

Calculate power

ST=sqrt(1+1)

Add terms

ST=sqrt(2)

The distance between S and T is sqrt(2). We can use a calculator to approximate its value. sqrt(2) ≈ 1.4