Let p=x^2+6
1 answer:
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reflection and translation.
Given:
The different transformation in the options.
To find:
The transformation that would result in the perimeter of a triangle being different from the perimeter of its image.
Solution:
In option 1,
It represents reflection across the line y=x.
In option 2,
It represents reflection across the x-axis.
In option 3,
It represents dilation by scale factor 4 and the center of dilation is at origin.
In option 4,
It represents translation 2 units right and 5 units down.
We know that the reflection and translation are rigid transformations, It means the size and shape of the figure remains the same after transformation.
So, the perimeter of the figure and its image are same in the case of reflection and translation.
But dilation is not a rigid transformation. In dilation, the figure is similar to its image. So, the perimeter of the figure and its image are different in the case of dilation.
Therefore, the correct option is 3.
In order to prove
Let's write both sides in terms of only.
Let's start with the left hand side: we can use the formula for sum and subtraction of the sine to write
and
So, their multiplication is
So, the left hand side simplifies to
Now, on with the right hand side. We have
Now simply make this expression one fraction:
And as you can see, the two sides are equal.