Question

what is the rule used to transform △abc to its image?
a(-3,5), b(2,8), c(-4,-5) and a(-3,-5), b(2,-8), c(-4,5)
a. ( r_m(x,y)=(-y,-x) ), where the equation of line ( m ) is ( y=-x )
b. ( r_n(x,y)=(y,x) ), where the equation of line ( n ) is ( y=-x )
c. ( r_{y - axis}(x,y)=(-x,y) )
d. ( r_{x - axis}(x,y)=(x,-y) )

Explanation:

Step1: Check each option

• For option A: \(r_{m}(x,y)=(-y,-x)\).
• Take point \(A(-3,5)\): \(r_{m}(-3,5)=(-5,3)

eq A'(-3,-5)\).

• For option B: \(r_{n}(x,y)=(y,x)\) where \(y = -x\).
• Take point \(A(-3,5)\): \(r_{n}(-3,5)=(5,-3)

eq A'(-3,-5)\).

• For option C: \(r_{y - axis}(x,y)=(-x,y)\).
• Take point \(A(-3,5)\): \(r_{y - axis}(-3,5)=(3,5)

eq A'(-3,-5)\).

• For option D: \(r_{x - axis}(x,y)=(x,-y)\).
• Take point \(A(-3,5)\): \(r_{x - axis}(-3,5)=(-3,-5)\).
• Take point \(B(2,8)\): \(r_{x - axis}(2,8)=(2,-8)\).
• Take point \(C(-4,-5)\): \(r_{x - axis}(-4,-5)=(-4,5)\).

Answer:

D. \(r_{x - axis}(x,y)=(x,-y)\)