Mike bought a soft drink for 2 dollars and 7 candy bars. He spent a total of 23 dollars. How much did each candy bar cost? Write
2 answers:
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The given transformation of reflection, rotation and translation are rigid transformation
The transformation that must take any point A to any point B are;
- <u>Rotation of 180° around the midpoint of segment AB</u>
- <u>Reflection across the perpendicular bisector</u>
- <u>Translation by the directed line segment AB</u>
Reason:
<em>Question: The given quadrilaterals ABCD and A'B'C'D' are congruent</em>
Required; To select all transformation that must take a point A to point B
Solution:
- Rotation of 180° around the midpoint of segment AB
A rotation of 180° about the midpoint of segment AB will change the places of points A and B
A(x, y) → R₁₈₀ → A'(-x, -y)
Let the coordinates of the origin be the midpoint of segment AB, and let (x, y) represent the coordinate of the point B(x, 0) we have;
∴ The coordinates of point A is A(-x, 0), which gives;
A(-x, 0) → R₁₈₀ → A'(x, 0) = point B
Therefore a rotation about the midpoint of AB must take point A to point B
- Reflection across the perpendicular bisector
The reflection of a point (x, y) about y-axis gives a point (-x, y), therefore, we have;
A(-x, 0) → Reflection across the y-axis → A'(x, 0) = point B
Therefore, a reflection across the perpendicular bisector of the line AB must take the point A to point B
- Translation by the directed line segment AB
A translation along the directed line segment AB of point A(-x, 0) 2·x units right gives;
A'(-x + 2·x, 0) = A'(x, 0) = Point B
Therefore, the transformations that must take any point A to any point B are;
<u>Rotation of 180° around the midpoint of segment AB</u>
<u>Reflection across the perpendicular bisector</u>
<u>Translation by the directed line segment AB</u>
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The height of the triangle if the base is 8 is 3.96 units
Given the following parameters
Base of a triangle = 8 units
Let the hypotenuse be "c"
Let the height be "h"
If the length of the hypotenuse of a right triangle is one unit more than twice the height, then;
c = 2h + 1
According to the Pythagoras theorem:
c² = b² + h²
(2h + 1)² = 8² + h²
Expand
4h²+4h+1 = 64 + h²
4h²-h² + 4h + 1 - 64 = 0
3h² + 4h - 63 = 0
Factorize the result
On factorizing, the value of the height is 2
h =
h = 11.89/3
h = 3.96 units
Hence the height of the triangle if the base is 8 is 3.96 units
Learn more here: brainly.com/question/20545047