Exercise 10 Page 59

We are given the slope between two points and asked to find one of the coordinates of the second point and the distance between these points. To do that we will use two formulas: the Slope Formula and the Distance Formula.

The value of n

The Slope Formula is used to determine the slope m of the line that connects two given points, ( x_1, y_1) and ( x_2, y_2). m=y_2- y_1/x_2- x_1 In this case, however, we have been given the slope of a line and two points with one missing coordinate. When we substitute these values into the Slope Formula, it does not matter which point we choose to use as ( x_1, y_1) or ( x_2, y_2). Both will give the same result. 5=n-( -1)/2-( -3) or 5=-1- n/-3- 2 Here we will use the points in the given order and solve for the unknown coordinate.

m = y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( -3,-1) & ( 2,n)

m=n-( -1)/2-( -3)

Substitute

m= 5

5=n-(-1)/2-(-3)

▼

Solve for n

SubNeg

a-(- b)=a+b

5=n+1/2+3

AddTerms

Add terms

5=n+1/5

MultEqn

LHS * 5=RHS* 5

25=n+1

SubEqn

LHS-1=RHS-1

24=n

RearrangeEqn

Rearrange equation

n=24

When n=24, the line passes through both points.

Distance

To find the distance between two points we can use the Distance Formula. AB=sqrt(( x_2- x_1)^2+( y_2- y_1)^2) Let's substitute A(-3,-1) and B=(2,24) into above formula.

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

SubstitutePoints

Substitute ( -3,-1) & ( 2,24)

AB=sqrt(( 2-( -3))^2+( 24-( -1))^2)

▼

Simplify

SubNeg

a-(- b)=a+b

AB=sqrt((2+3)^2+(24+1)^2)

AddTerms

Add terms

AB=sqrt((5)^2+(25)^2)

CalcPow

Calculate power

AB=sqrt(25+625)

AddTerms

Add terms

AB=sqrt(650)

UseCalc

Use a calculator

AB=25.49509...

RoundDec

Round to 1 decimal place(s)

AB≈25.5

The distance between A and B is approximately 25.5.