Question

4 - 21. plot ( \triangle abc ) on graph paper with points ( a(2,2) ), ( b(-2,-2) ), and ( c(8,-2) ).
a. use the function ( (x,y)\to(-1x,-1y) ) to transform ( \triangle abc ). graph and connect the new points then label this triangle ( \triangle abc ). describe how ( \triangle abc ) has been transformed. what, if anything, about the original triangle has been preserved in its image?
b. now use the function ( (x,y)\to(-2x,-2y) ) to transform the original ( \triangle abc ) to create ( \triangle abc ). has ( \triangle abc ) undergone a rigid transformation to create ( \triangle abc )? what, if anything, about the original triangle has been preserved in its image?
4 - 22. rewrite each of the following products as a sum by using the distributive property.
a. ( 5x(x - 6) )
b. ( -9y(6 - 3y) )

Explanation:

4 - 22

a.

Step1: Apply the distributive property \(a(b + c)=ab+ac\)

Here \(a = 5x\), \(b=x\), and \(c=-6\). So, \(5x(x - 6)=5x\times x+5x\times(- 6)\)

Step2: Simplify the terms

Using the rule of exponents \(x^m\times x^n=x^{m + n}\), \(5x\times x = 5x^{1+1}=5x^{2}\), and \(5x\times(-6)=-30x\)

Step1: Apply the distributive property \(a(b + c)=ab+ac\)

Here \(a=-9y\), \(b = 6\), and \(c=-3y\). So, \(-9y(6-3y)=-9y\times6+(-9y)\times(-3y)\)

Step2: Simplify the terms

\(-9y\times6=-54y\), and using the rule of exponents \(x^m\times x^n=x^{m + n}\) and \((-a)\times(-b)=ab\), \((-9y)\times(-3y)=27y^{1 + 1}=27y^{2}\)

Answer:

\(5x^{2}-30x\)

b.