Exercise 19 Page 437

To find the distance between the given points, we can use the Distance Formula. d=sqrt(( x_2- x_1)^2+( y_2- y_1)^2) Let's substitute the given coordinates, P( - 9 14, - 7 12) and Q( - 4, 5) into this formula and simplify.

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

SubstitutePoints

Substitute ( - 9 14, - 7 12) & ( - 4, 5)

d=sqrt(( - 4-( - 9 14))^2+( 5-( - 7 12))^2)

SubNeg

a-(- b)=a+b

d=sqrt((- 4+9 14)^2+(5+ 7 12)^2)

MixedToFrac

a bc=a* c+b/c

d=sqrt((- 4+ 9* 4+14)^2+(5+ 7* 2+12)^2)

NumberToFrac

a = 4* a/4

d=sqrt((- 4* 4/4+9* 4+1/4)^2+(5* 4/4+ 7* 2+1/2)^2)

Multiply

d=sqrt((- 16/4+36+1/4)^2+(20/4+ 14+1/2)^2)

AddTerms

Add terms

d=sqrt((- 16/4+37/4)^2+(20/4+ 15/2)^2)

ExpandFrac

a/b=a * 2/b * 2

d=sqrt((- 16/4+37/4)^2+(20/4+ 15* 2/2* 2)^2)

Multiply

d=sqrt((- 16/4+37/4)^2+(20/4+ 30/4)^2)

MoveNegFracToNum

Put minus sign in numerator

d=sqrt((- 16/4+37/4)^2+(20/4+ 30/4)^2)

AddFrac

Add fractions

d=sqrt((- 16+37/4)^2+(20+30/4)^2)

AddTerms

Add terms

d=sqrt((21/4)^2+(50/4)^2)

PowQuot

(a/b)^m=a^m/b^m

d=sqrt(21^2/4^2+50^2/4^2)

CalcPow

Calculate power

d=sqrt(441/16+2500/16)

AddFrac

Add fractions

d=sqrt(441 + 2500/16)

AddTerms

Add terms

d=sqrt(2941/16)

SqrtQuot

sqrt(a/b)=sqrt(a)/sqrt(b)

d=sqrt(2941)/sqrt(16)

CalcRoot

Calculate root

d=54.230987 .../4

UseCalc

Use a calculator

d=13.557746 ...

RoundDec

Round to 1 decimal place(s)

d=13.6

The points are about 13.6 units apart.

Hints

Check the answer

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