Exercise 50 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 (0,3) and the coordinate for B is (-2,-2). 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 ( 0,3) & ( -2,-2)

d=sqrt(( -2- 0)+( -2- 3)^2)

SubTerms

Subtract terms

d=sqrt((-2)^2+(-5)^2)

CalcPow

Calculate power

d=sqrt(4+25)

AddTerms

Add terms

d=sqrt(29)

UseCalc

Use a calculator

d≈ 5.4

The distance between points A and B is approximately 5.4.

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 ( 0,3) & ( -2,-2)

M(0+( -2)/2,3+( -2)/2)

AddNeg

a+(- b)=a-b

M(0-2/2,3-2/2)

SubTerms

Subtract terms

M(-2/2,1/2)

Div

Divide by 2

M(-1,0.5)

The midpoint of line segment AB is the point (-1,0.5).

Subchapter links

Lesson Check p.53

Practice and Problem-Solving Exercises p.54-56

Standardized Test Prep p.56

Mixed Review p.56

Exercise 50 Page 55

Hints

Check the answer

Practice exercises

Asses your skill