The second matrix
represents the triangle dilated by a scale factor of 3.
Step-by-step explanation:
Step 1:
To calculate the scale factor for any dilation, we divide the coordinates after dilation by the same coordinated before dilation.
The coordinates of a vertice are represented in the column of the matrix. Since there are three vertices, there are 2 rows with 3 columns. The order of the matrices is 2 × 3.
Step 2:
If we form a matrix with the vertices (-2,0), (1,5), and (4,-8), we get
![\left[\begin{array}{ccc}-2&1&4\\0&5&-8\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%261%264%5C%5C0%265%26-8%5Cend%7Barray%7D%5Cright%5D)
The scale factor is 3, so if we multiply the above matrix with 3 throughout, we will get the matrix that represents the vertices of the triangle after dilation.
Step 3:
The matrix that represents the triangle after dilation is given by
![3\left[\begin{array}{ccc}-2&1&4\\0&5&-8\end{array}\right] = \left[\begin{array}{ccc}3(-2)&3(1)&3(4)\\3(0)&3(5)&3(-8)\end{array}\right] = \left[\begin{array}{ccc}-6&3&12\\0&15&-24\end{array}\right]](https://tex.z-dn.net/?f=3%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%261%264%5C%5C0%265%26-8%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%28-2%29%263%281%29%263%284%29%5C%5C3%280%29%263%285%29%263%28-8%29%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-6%263%2612%5C%5C0%2615%26-24%5Cend%7Barray%7D%5Cright%5D)
This is the second option.
The pythagorean theorem states that for any RIGHT-ANGLED TRIANGLE, the relationship between the side lengths are A²+B²=C², where C is the hypotenuse :P
Which means that it can only be applied on right angled triangles~
So your answer would be B, a right-angled triangle.
Ask me if you are unsure about anything <3
Do 25 divided by 1/2 to get your answer. Thanks! Brainly Team
The lengths of the first, second and third piece are respectively 8 ft, 16 ft and 32 ft
<h3>How to solve Algebra word Problems?</h3>
Let the length of the first piece be x.
Let the length of the second piece be 2x
Let the length of the thrid piece be 4x
Since the total length of the piece is 56 ft, then we can say that;
x + 2x + 4x = 56
7x = 56
x = 56/7
x = 8 ft
Thus, length of first piece = 8 ft
Length of second piece = 2 * 8 = 16 ft
Length of third piece = 4 * 8 = 32 ft
Thus, the lengths of the first, second and third piece are respectively 8 ft, 16 ft and 32 ft
Read more about Algebra Word Problems at; brainly.com/question/13818690
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