Question 2(Multiple Choice Worth 4 points)
1 answer:
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The dimensions of the image are twice the dimensions of the preimage,
which indicates that the transformation is a dilation.
- The transformation <em>T</em> is; <u>a dilation transformation with a scale factor of 2, D₂</u>
Reasons:
The transformation applied to ΔABC = T
The image of ΔABC following the transformation, T = ΔA'B'C'
The perimeter of ΔA'B'C' = Twice the perimeter of ΔABC
Therefore, we have;
A'B' + B'C' + A'C' = 2 × (AB + BC + AC)
Which gives
A'B' + B'C' + A'C' = 2·AB + 2·BC + 2·AC
By similar triangles, we have the ratio of corresponding sides as follows;
Which gives;
A'B' = 2·AB
Therefore;
- Triangle ΔA'B'C' is twice the dimension of triangle ΔABC, and <em>T</em> is <u>a dilation transformation with a scale factor of 2, D₂</u>
Learn more about dilation transformation here:
Answer:
B. 1.4 feet
Step-by-step explanation:
Let, the amount of increase be 'x' ft.
Since, the length and width of the canvas are 4 ft and 3 ft respectively.
Thus, area of the canvas, = length × breadth = 4 × 3 = 12 ft²
Since, the area of display model is twice the area of the canvas. We have,
= 2 ×
i.e. = 2 × 12
i.e. = 24 ft².
As, the length and width of the canvas are increased by 'x'.
The, length and width of the display model are (x+4) ft and (x+3) ft.
So, we get,
= length × breadth = (x+4) × (x+3) =
Since, = 24 ft²
i.e. = 24
i.e.
Solving the quadratic equation, we get,
i.e. x = -8.4 and x= 1.4
Since, the value of x cannot be negative.
Thus, x = 1.4 feet.