Answer:
- The sequence of transformations that maps triangle XYZ onto triangle X"Y"Z" is <u>translation 5 units to the left, followed by translation 1 unit down, and relfection accross the x-axis</u>.
Explanation:
By inspection (watching the figure), you can tell that to transform the triangle XY onto triangle X"Y"Z", you must slide the former 5 units to the left, 1 unit down, and, finally, reflect it across the x-axys.
You can check that analitically
Departing from the triangle: XYZ
- <u>Translation 5 units to the left</u>: (x,y) → (x - 5, y)
- Vertex X: (-6,2) → (-6 - 5, 2) = (-11,2)
- Vertex Y: (-4, 7) → (-4 - 5, 7) = (-9,7)
- Vertex Z: (-2, 2) → (-2 -5, 2) = (-7, 2)
- <u>Translation 1 unit down</u>: (x,y) → (x, y-1)
- (-11,2) → (-11, 2 - 1) = (-11, 1)
- (-9,7) → (-9, 7 - 1) = (-9, 6)
- (-7, 2) → (-7, 2 - 1) = (-7, 1)
- <u>Reflextion accross the x-axis</u>: (x,y) → (x, -y)
- (-11, 1) → (-11, -1), which are the coordinates of vertex X"
- (-9, 6) → (-9, -6), which are the coordinates of vertex Y""
- (-7, 1) → (-7, -1), which are the coordinates of vertex Z"
Thus, in conclusion, it is proved that the sequence of transformations that maps triangle XYZ onto triangle X"Y"Z" is translation 5 units to the left, followed by translation 1 unit down, and relfection accross the x-axis.
Answer: 3/4
Step-by-step explanation:
Graph the line using the slope and y-intercept, or two points.
Slope: 3/4
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The will spend $33.60 (option C) to make the figure out of construction paper, if the construction paper cost $0.10 per square inch.
Step-by-step explanation:
The given is,
Construction paper cost $0.10 per square inch
Pyramid diagram with dimensions
Step:1
Formula to calculate the area of pyramid,
..............(1)
Where,
l - Base length
w - Base width
h - Height of pyramid
From given,
l = 12 inches
w = 12 inches
For height of pyramid,
By using Pythagorean theorem,
.................(2)
For right angle triangle,
Base =
= 6 inches
Equation (2) becomes,




Height = 5.2915 inches
h - 5.2915 inches
Equation (1) becomes,




≅ 336 square inches
Where,
$0.10 per square inch ( from given)
Paper cost of total figure = 336 square inches
= 336 × 0.10
= $ 33.60
Result:
The will spend $33.60 to make the figure out of construction paper, if the construction paper cost $0.10 per square inch.