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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

Maintaining Mathematical Proficiency

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Exercise 1 Page 585

Recall the Midpoint and the Distance Formulas.

Midpoint: M(-2,4)
Distance: about 7.2 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 (-4,1) and (0,7). Let's use these to find the coordinates of the midpoint.

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

SubstitutePoints

Substitute ( -4,1) & ( 0,7)

M(-4+ 0/2,1+ 7/2)

Add terms

M(-4/2,8/2)

Calculate quotient

M(-2,4)

The midpoint is located at (-2,4).

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, P(-4,1) and Q(0,7), into this formula and simplify.

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

SubstitutePoints

Substitute ( -4,1) & ( 0,7)

d=sqrt(( 0-( -4))^2+( 7- 1)^2)

a-(- b)=a+b

d=sqrt(4^2+(7-1)^2)

Subtract term

d=sqrt(4^2+6^2)

Calculate power

d=sqrt(16+36)

Add terms

d=sqrt(52)

Use a calculator

d≈7.2

The distance between P and Q is sqrt(52), which is approximately 7.2 units.

Subchapter links

Exercises p.585