Exercise 9 Page 553

Let's draw FF'.

According to the Coordinate Rules for Reflection, if (a,b) is reflected in y=- x, then it's image is the point (- b, - a). Since F=(- 2 ,1) it must be that F'= (- ( - 2), - 1) = (2,- 1). Now we can calculate the slope using the Slope Formula.

m = y_2 - y_1/x_2 - x_1

SubstitutePoints

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

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

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Simplify RHS

SubNeg

a-(- b)=a+b

m = 1 - 2/- 2 + 1

AddSubTerms

Add and subtract terms

m = - 1/- 1

DivNegNeg

- a/- b=a/b

m = 1/1

QuotOne

a/a=1

m = 1

If FF' is perpendicular to y=- x then the product of their slopes will equal - 1.

m_1* m_2=- 1

SubstituteII

m_1= 1, m_2= - 1

1( - 1)? =- 1

OneMult

1* a=a

- 1=- 1

FF' is perpendicular to y=- x.