Answer:
Step-by-step explanation:
- Diagonals of a rhombus are perpendicular.
- Sides are of equal length.
<u>Use Pythagorean to work out the side length.</u>
- a² = (d₁/2)² + (d₂/2)²
- a² = (24/2)² + (45/2)² = 650.25
- a = √650.25
- a = 25.5 cm
<u>The perimeter is:</u>
- P = 4a
- P = 4*25.5 = 102 cm
Answer:
A′B′ and AB are equal in length.
Step-by-step explanation:
Given that the location of the points are at A(1, 3) and B(5, 3).
Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, translation and dilation.
Rigid transformation are transformation that preserves the shape and size when performed. Types of rigid transformation are reflection, rotation, translation.
Hence if AB is rotated 270 degrees counterclockwise about the origin to form A′B′, both A′B′ and AB are equal in length because rotation is a rigid transformation.
If A(x,y) is rotated 270 degrees counterclockwise about the origin, it becomes A'(y,-x).
Hence if AB is rotated 270 degrees counterclockwise about the origin to form A'(3, -1), B'(3, -5)
I believe since the definition of perimeter is adding the lengths of all three sides of the angles the, width of the rectangle would be 5, and the length of the rectangle would be 10.
10
+10
-------
20
+5
------
25
+5
------
30
And that is you answer, yay!
The easy part is isolating the absolute-value term:
5 + 7 |2<em>x</em> - 1| = -44
7 |2<em>x</em> - 1| = -49
|2<em>x</em> - 1| = -7
Remember that the absolute value function returns a positive number that you can think of as the "size" of that number, or the positive distance between that number and zero. If <em>x</em> is a positive number, its absolute value is the same number, |<em>x</em>| = <em>x</em>. But if <em>x</em> is negative, then the absolute value returns its negative, |<em>x</em>| = -<em>x</em>, which makes it positive. (If <em>x</em> = 0, you can use either result, since -0 is still 0.)
The important thing to take from this is that there are 2 cases to consider: is the expression in the absolute value positive, or is it negative?
• If 2<em>x</em> - 1 > 0, then |2<em>x</em> - 1| = 2<em>x</em> - 1. Then the equation becomes
2<em>x</em> - 1 = -7
2<em>x</em> = -6
<em>x</em> = -3
• If 2<em>x</em> - 1 < 0, then |2<em>x</em> - 1| = - (2<em>x</em> - 1) = 1 - 2<em>x</em>. Then
1 - 2<em>x</em> = -7
-2<em>x</em> = -8
<em>x</em> = 4
