Given:
Consider triangle ABC is rotated 90 degrees counterclockwise and then translated 3 units up to form triangle A'B'C'.
To find:
The transformation that can be used to map each point (x,y) on Triangle ABC to its corresponding point on Triangle A'B'C'.
Solution:
If a figure rotated 90 degrees counterclockwise, then
If a figure translated 3 units up, then
If triangle ABC is rotated 90 degrees counterclockwise and then translated 3 units up to form triangle A'B'C', then the rule of transformation is
Therefore, the required rule of transformation is .
Note: Option are not in proper form.
Answer:
Step-by-step explanation:
For any triangle, the Law of Cosines is given by 
, where all three variables are interchangeable.
Therefore, we have:
When you multiply exponential expressions that have the same base, you simply add the exponents. This is true for both numbers and variables. When you include other numbers in the multiplication, you simply factor and break the expression into several multiplications.
2^5 * 2^x= 2^(5 + X)
Answer:
1) (x, y) = (1, 8)
2) (x, y) =<em>(-2, -4)</em>
3) (x, y) = (3, -1)
Step-by-step explanation:
1) Given the equations;
7x+2y =23 .... 1
6x+y= 14 .... 2
From 2; y = 14-6x
Substitute into 1;
From 1; 7x+2y =23
7x + 2(14-6x) = 23
7x + 28 - 12x = 23
-5x = 23 - 28
-5x = -5
x = 5/5
x = 1
Substitute x = 1 into y = 14-6x
y = 14 - 6 (1)
y - 14 - 6
y = 8
Hence (x, y) = (1, 8)
2) Given
y=-4
y=-3x-10
We will simply equate bith expression and get x;
-3x - 10 = -4
-3x = -4 + 10
-3x = 6
x = 6/-3
x = -2
<em>Hence the solution is (-2, -4)</em>
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3) Given the equation
y=-3x+8
y=5x-16
Equate both expressions;
-3x + 8 = 5x - 16
-3x - 5x = -16 - 8
-8x = -24
x = 24/8
x = 3
Substitute x = 3 into y=-3x+8
y = -3(3) + 8
y = -9 + 8
y = -1
Hence the solution (x, y) = (3, -1)
