Question

1. if a rectangle has an area of 36 units, then its perimeter is 26 units.

a. accurately draw and label an instance of this statement.
b. accurately draw and label a counterexample of this statement.

1. a. (r_{x - axis}(3,5)=) b. (r_{y - axis}(3,5)=

summer math skills sharpener - prealgebra
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Explanation:

Step1: For 6a, find rectangle dimensions

Let length $l = 9$ and width $w = 4$, area $A=l\times w=9\times4 = 36$, perimeter $P = 2(l + w)=2(9 + 4)=26$. Draw rectangle with sides 9 and 4.

Step2: For 6b, find counter - example

Let $l = 12$ and $w = 3$, $A = 12\times3=36$, $P=2(12 + 3)=30
eq26$. Draw rectangle with sides 12 and 3.

Step3: For 7a, reflection over x - axis

The rule for reflecting $(x,y)$ over x - axis is $(x,-y)$. So $r_{x - axis}(3,5)=(3, - 5)$.

Step4: For 7b, reflection over y - axis

The rule for reflecting $(x,y)$ over y - axis is $(-x,y)$. So $r_{y - axis}(3,5)=(-3,5)$.

Answer:

6a: Draw rectangle with sides 9 and 4.
6b: Draw rectangle with sides 12 and 3.
7a: $(3, - 5)$
7b: $(-3,5)$