Exercise 7 Page 435

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, K( 8 12, 12) and L( - 6 34, 7 12) into this formula and simplify.

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

SubstitutePoints

Substitute ( 8 12, 12) & ( - 6 34, 7 12)

d=sqrt(( - 6 34- 8 12)^2+( 7 12- 12)^2)

MixedToFrac

a bc=a* c+b/c

d=sqrt((- 6* 4+3/4-8* 2+1/2)^2+(7* 2+ 1/2-12)^2)

NumberToFrac

a = 4* a/4

d=sqrt((- 6* 4+3/4-8* 2+1/2)^2+(7* 2+ 1/2-12* 4/4)^2)

Multiply

d=sqrt((- 24+3/4-16+1/2)^2+(14+ 1/2-48/4)^2)

AddTerms

Add terms

d=sqrt((- 27/4-17/2)^2+(15/2-48/4)^2)

MoveNegFracToNum

Put minus sign in numerator

d=sqrt((- 27/4-17/2)^2+(15/2-48/4)^2)

ExpandFrac

a/b=a * 2/b * 2

d=sqrt((- 27/4-17* 2/2* 2)^2+(15* 2/2* 2-48/4)^2)

Multiply

d=sqrt((- 27/4-34/4)^2+(30/4-48/4)^2)

SubFrac

Subtract fractions

d=sqrt((- 27-34/4)^2+(30-48/4)^2)

SubTerms

Subtract terms

d=sqrt((- 61/4)^2+(- 18/4)^2)

MoveNegNumToFrac

Put minus sign in front of fraction

d=sqrt((- 61/4)^2+(- 18/4)^2)

NegBaseToPosPow

(- a)^2 = a^2

d=sqrt((61/4)^2+(18/4)^2)

PowQuot

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

d=sqrt(61^2/4^2+18^2/4^2)

CalcPow

Calculate power

d=sqrt(3 721/16+324/16)

AddFrac

Add fractions

d=sqrt(3 721+324/16)

AddTerms

Add terms

d=sqrt(4 045/16)

SqrtQuot

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

d=sqrt(4 045)/sqrt(16)

CalcRoot

Calculate root

d=63.600314 .../4

UseCalc

Use a calculator

d=15.900078 ...

RoundDec

Round to 1 decimal place(s)

d=15.9

The points are about 15.9 units apart.

Hints

Check the answer

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