Which statement is true about the product of a non-zero rational number and an irrational number?
1 answer:
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Given:
The three vertices of a parallelogram are (-3,8), (4,5), (2,-5).
To find:
The fourth vertex of the parallelogram.
Solution:
Let the vertices of the parallelogram are A(-3,8), B(4,5), C(2,-5) and D(a,b).
We know that, diagonals of a parallelogram bisect each other. It means midpoints of both diagonals are same.
Midpoint formula:
Two diagonals of ABCD are AC and BD.
Midpoint of AC = Midpoint of BD
On comparing both sides, we get
And,
Therefore, the coordinates of fourth vertex are (-5,-2).
Answer:
x = 41.2
Step-by-step explanation:
Assuming the dotted line at the top is parallel to the segment with length x, it follows from the alternate interior angles theorem that the interior angle of the triangle (marked in diagram) is also 27º.
Using SOH-CAH-TOA, we get that tan(27º) = 21/x, so x = 21/tan(27º), which is approximately equal to 41.2.
