Answer:
Maybe D
Step-by-step explanation:
The diamond is 1 the square is 6 and the triangle is 7
We know that
Rigid transformation:
A rigid transformation (also called an isometry) is a transformation of the plane that preserves length.
Reflections, translations, rotations, and combinations of these three transformations are "rigid transformations"
so, it's length must be preserved
now, we will check each option
option-A:
we have (x,3y)
y-value changes but x-value will remain same
It changes length
so, this is not rigid transformation
option-B:
we have (3x,y)
x-value changes but y-value will remain same
It changes length
so, this is not rigid transformation
option-C:
(2x, y+2)
It changes length of x-value
but it is only shifting y-value
so, it changes length
so, this is not rigid transformation
option-D:
Both shifts values
but it's length will always be same
so, this is rigid transformation..............Answer
The formula for volume of a prism is v=(1/2bh)h so it would be
(1/2 ×7.8×4)×9= 140.4
The formula of linear equation is:
![y1 - y2 = m(x1 - x2)](https://tex.z-dn.net/?f=y1%20%20-%20%20y2%20%3D%20m%28x1%20%20-%20%20x2%29)
Where
x1 and x2: x coordinates(-1 and 3)
y1 and y2: y coordinates(-2 and 10)
m is the slope
We can then choose a point from the line to find the eqaution.
We need to first find the slope:
![\frac{y1 - y2}{x1 - x2}](https://tex.z-dn.net/?f=%20%5Cfrac%7By1%20-%20y2%7D%7Bx1%20-%20x2%7D%20)
In this case:
![\frac{ - 2 - 10}{ - 1 - 3} \\ = \frac{ - 12}{ - 4} \\ = 3](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20-%202%20-%2010%7D%7B%20-%201%20-%203%7D%20%20%20%5C%5C%20%3D%20%20%5Cfrac%7B%20-%2012%7D%7B%20-%204%7D%20%20%5C%5C%20%20%3D%203)
In this case, as the y2 is given as 1,put (-1,-2) , and the slope(3 )into the eqaution :
y-(-2) = 3(x-(-1))
y+2 = 3(x+1)
Therefore
![y + 2 = 3x + 1](https://tex.z-dn.net/?f=y%20%2B%202%20%3D%203x%20%2B%201)
is the answer.
Hope it helps!