Which rigid motion does not preserve orientation

1 answer:

4 0

I think that translation is the only one that DOES preserve orientation.
Rotation and reflection definitely don't, and I'm not sure about dilation.

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What are the y and x intercepts of y=3(x-6)²-9 and y=-2(x+5)²+3 .. Thanks

JulsSmile [24]

1.
$y=3(x-6)^2-9 \\ \\
\hbox{x-intercept - y=0} \\
0=3(x-6)^2-9 \\
9=3(x-6)^2 \ \ \ |\div 3 \\
3=(x-6)^2 \\
\sqrt{3}=\sqrt{(x-6)^2} \\
\pm \sqrt{3}=x-6 \\
\pm \sqrt{3}+6=x \\
x=6+\sqrt{3} \ \lor \ x=6-\sqrt{3}} \\ \\
\hbox{y-intercept - x=0} \\
y=3(0-6)^2-9 \\
y=3 \times (-6)^2-9 \\
y=3 \times 36-9 \\
y=108-9 \\
y=99 \\ \\
\boxed{\hbox{x-intercepts: } 6+\sqrt{3} \hbox{ and } 6-\sqrt{3}} \\
\boxed{\hbox{y-intercept: } 99}$

2.
$y=-2(x+5)^2+3 \\ \\
\hbox{x-intercept - y=0} \\
0=-2(x+5)^2+3 \\
-3=-2(x+5)^2 \ \ \ |\div (-2) \\
\frac{3}{2}=(x+5)^2 \\
\sqrt{\frac{3}{2}}=\sqrt{(x+5)^2} \\
\pm \sqrt{\frac{3}{2}}=x+5 \\
\pm \sqrt{\frac{3}{2}}-5=x \\
x=\sqrt{\frac{3}{2}}-5 \ \lor \ x=-\sqrt{\frac{3}{2}}-5 \\ \\
\hbox{y-intercept - x=0} \\
y=-2(0+5)^2+3 \\
y=-2 \times 5^2 +3 \\
y=-2 \times 25+3 \\
y=-50+3 \\
y=-47 \\ \\ \boxed{\hbox{x-intercepts: } \sqrt{\frac{3}{2}}-5 \hbox{ and } -\sqrt{\frac{3}{2}}-5} \\ \boxed{\hbox{y-intercept: } -47}$

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damaskus [11]

Try using Photomath for these types of problems

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Choose the function with the largest constant of variation? A 2-column table with 5 rows. Column 1 is labeled x with entries 1,

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Answer:

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Step-by-step explanation:

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Art and his friends spent $62 at the movies. Admission tickets cost $12 apiece, and a bucket of popcorn costs $7. Which equation

Darya [45]

Answer: 12t+7p=62

Step-by-step explanation:

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3 years ago

Find the complete area for the shape below.

posledela

Answer:

42.5units^2

Step-by-step explanation:

Area of a trapezium=1/2 *(a+b) height.

a=5 units

b=12units

height=5units

Area=1/2*(5+12)*5

Area=1/2*17*5

Area=1/2*85

Area=42.5units^2

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