Exercise 49 Page 55

Practice makes perfect

a AB is the distance between points A and B. To find this distance, let's start by finding the coordinates of the points on the graph.

The coordinate for A is (-2,-2) and the coordinate for B is (8,-6). Now we can use the Distance Formula. d=sqrt((x_2-x_1)^2+(y_2-y_1)^2) Let's substitute our points into this formula and simplify.

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

SubstitutePoints

Substitute ( 8,-6) & ( -2,-2)

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

SubNeg

a-(- b)=a+b

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

AddSubTerms

Add and subtract terms

d=sqrt((-10)^2+4^2)

CalcPow

Calculate power

d=sqrt(100+16)

AddTerms

Add terms

d=sqrt(116)

UseCalc

Use a calculator

d≈10.8

The distance between points A and B is approximately 10.8.

b Now, we want to find the midpoint of line segment AB. We can do this using the Midpoint Formula.

M ( x_1+x_22, y_1+y_22) Let's substitute our points into the formula and simplify.

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

SubstitutePoints

Substitute ( 8,-6) & ( -2,-2)

M(8+( -2)/2,-6+( -2)/2)

AddNeg

a+(- b)=a-b

M(8-2/2,-6-2/2)

SubTerms

Subtract terms

M(6/2,-8/2)

Div

Divide by 2

M(3,-4)

The midpoint of line segment AB is the point (3,-4).

Subchapter links

Lesson Check p.53

Practice and Problem-Solving Exercises p.54-56

Standardized Test Prep p.56

Mixed Review p.56

Exercise 49 Page 55

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