The vertices of polygon ABCD are at A(1,1), B(2,3), C(3,2), and D(2,1). ABDC is reflected across the x-axis and translated 2 uni
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Given:
A figure of a parallelogram.
The vertex angles are .
To find:
The values of a and b.
Solution:
We know that the pairs of consecutive angles of a parallelogram are supplementary angles. It mean their sum is 180 degrees.
(Supplementary angles)
Subtract 10 from both sides.
Divide both sides by 17.
Now,
And,
(Supplementary angles)
Divide both sides by 2.
Therefore, the value of a is 64 and the value of b is 10.
I would use a chart to solve this problem.
This is a good wya to organize your information.
Down the left side, list the people involved.
I put Bob first and the mom second but the order doesn't matter.
Since Bob's mom is 3 times older than Bob, we can represent
Bob's age now as x and Bob's mom's age now as 3x.
Bob's age in 12 years will be x + 12 and Bob's mom's
age in 12 years will simply be 3x + 12.
Since the second sentence starts with in 12 years,
we will be using the information from our second column.
In 12 years, Bob's mom's age, 3x + 12, will be,
equals, twice of her son's age, 2(x + 12).
Solving from here, we find that x = 12.
This means that Bob's age now is 12 and his mom is 36.
The chart is attached below.
